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All Textbook Solutions for Elementary Geometry for College Students

15CR 16CR 17CR Name the longest line segment shown in quadrilateral ABCD.19CR Two sides of a triangle have lengths 15 and 20. The length of the third side can be any number between ?_ and ?_.21CR 22CR 23CR 24CR Given: ABC is isosceles with base AB AB=y+7BC=3y+5AC=9y Find: Whether ABC is also equilateral Exercises 25, 26 26CR 27CR Construct a right triangle that has acute angle A and hypotenuse of length c.Construct a second isosceles triangle in which the base angles are half as large as the base angles of the given isosceles triangle.It is given that ABCDEF triangles not shown a If mA=37 and mE=68, find mF. _ b If AB=7.3cm, BC=4.7cm, and AC=6.3cm, find EF. _Consider XYZ triangles not shown a Which side is included by X and Y?_ b Which angle is included by sides XY and YZ?_3CT 4CT With congruent parts marked, are the two triangles congruent? a ABC and DAC_ b RSM and WVM_6CT 7CT CM is the median for ABC from vertex C to side AB. a Name two line segments that must be congruent. _ b Is 1 necessarily congruent to 2?_9CT 10CT 11CT Show all arcs in the following construction. Construct an isosceles right triangle in which each leg has the length of line segment AB.13CT 14CT 15CT 16CT Complete all statements and reasons for the following proof problem. Given: R and V are right angles;12 Prove: RSTVST PROOF Statements Reasons Complete all missing statements and reasons in the following proof. Given: RUVRV and 13 Prove: STU is an isosceles triangle Proof Statements Reasons 1. RUV;RV 1. 2. UVUR 2. 3. 3. Given 4. RSUVTU 4. 5. 5. CPCTC 6 6. If 2 sides of a are , this triangle is an isosceles triangle.The perimeter of an isosceles triangle is 32cm. If the length of the altitude drawn to the base is 8cm, how long is each leg of the isosceles triangle?_ABCD is a parallelogram. a Using a ruler, compare the lengths of sides AB- and DC-. b Using a protractor, compare the measures of A and C.ABCD is a parallelogram. a Using a ruler, compare the lengths of sides AD- and BC-. b Using a protractor, compare the measures of B and D.MNPQ is a parallelogram. Suppose that MQ=5, MN=8, and mM=1100. Find: a QP c mQ b NP d mP MNPQ is a parallelogram. Suppose that MQ=12.7, MN=17.9, and mM=1220. Find: a QP c mQ b NP d mP For Exercises 5 to 8, MNPQ is a parallelogram with diagonals QN- andMP-. a If QN=12.8, find QR. b If MR=5.3, find MP.For Exercises 5 to 8, MNPQ is a parallelogram with diagonals QN- andMP-. a If QR=7.3, find RN. b If MP=10.6, find RP.For Exercises 5 to 8, MNPQ is a parallelogram with diagonals QN- andMP-. If QR=2x+3 and RN=x+7, find QR, RN, and QN.For Exercises 5 to 8, MNPQ is a parallelogram with diagonals QN- andMP-. If MR=5a+7 and MP=12a+34, find MR, RP, and MP.Given that AB=3x+2, BC=4x+1, and CD=5x-2, find the length of each side of .Given that mA=2x+3, and mC=3x-27, find the measure of each angle of .Given that mA=2x+3, and mB=3x-23, find the measure of each angle of .Given that mA=2x5, and mB=x2, find the measure of each angle of. ABCD.Given that mA=2x3, and mC=x2+20, find the measure of each angle of ABCD.Given that mA=2x+y, mB=2x+3y-20, and mC=3x-y+16, find the measure of each angle of .Assuming that mBmA in , which diagonal AC-orBD- would be longer?Suppose that diagonals AC-andBD- of are drawn and that ACBD. Which angle A or B would have the greater measure?In Exercises 17 and 18, consider with VX- RS- and VY- ST-. a Which line segment is the altitude of with respect to base ST-? b Which number is the height of with respect to base ST-?In Exercises 17 and 18, consider with VX- RS- and VY- ST-. a Which line segment is the altitude of with respect to base RS-? b Which number is the height of with respect to base RS-?In Exercises 19 to 22, classify each statement as true or false. In Exercises 19 to 20, recall that the symbol means is a subset of. Where Q=quadrilaterals and P=polygons, QP.20E 21E 22E In quadrilateral RSTV, the midpoints of consecutive sides are joined in order. Try drawing other quadrilaterals and joining their midpoints. What can you conclude about the resulting quadrilateral in each case?In quadrilateral ABCD, the midpoints of opposite sides are joined to form two intersecting segments. Try drawing other quadrilaterals and joining opposite midpoints. What can you conclude about these segments in each case?Quadrilateral ABCD has AB-DC- and AD-BC-. Using intuition, what type of quadrilateral is ABCD?Quadrilateral RSTV has RS-TV- and RS-TV-. Using intuition, what type of quadrilateral is RSTV?In Exercises 27-30, use the definition of a parallelogram to complete each proof. Given:RS-VT-, RV-VT-, and ST-VT- Prove: RSTV is a parallelogram PROOF Statements Reasons 1. RS-VT- 1.? 2.? 2.Given 3.? 3.If two lines are to the same line, they are , to each other 4.? 4.If both pairs of opposite side of a quadrilateral are , the quadrilateral is a 28E In Exercises 27 to 30, use the definition of a parallelogram to complete each proof. Given: Parallelogram RSTV; also XY-VT- Prove: 1S Plan: First show that RSYX is a parallelogram.In Exercises 27-30, use the definition of a parallelogram to complete each proof. Given: Parallelogram ABCD with DE-AB- and FB-AB- Prove: DE-FB- Plan: First show that DEBF is a parallelogram.31E In Exercises 31 to 34, write a formal proof of each theorem or corollary. The opposite sides of a parallelogram are congruent.33E 34E The bisectors of two consecutive angles of HJKL are shown. What can you conclude regarding P?When the bisectors of two consecutive angles of a parallelogram meet at a point on the remaining side, what type of triangle is: a DEC? b ADE? c BCE?Draw parallelogram RSTV with mR=700 and mS=1100. Which diagonal of RSTV has the greater length?Draw parallelogram RSTV so that the diagonals have the lengths RT=5 and SV=4. Which two angles of RSTV have the greater measure?The following problem is based on the Parallelogram Law. In the scaled drawing, each unit corresponds to 50 mph. A small airplane travels due east at 250 mph. The wind is blowing at 50 mph in the direction due north. Using the indicated diagonal and use it to determine the speed of the airplane in miles per hour.In the drawing for Exercise 41, the bearing direction in which the airplane travels is described as north x0 east, where x is the measure of the angle from the north axis towards the east axis. Using a protector, find the approximate bearing of the airplane.Two streets meet to form an obtuse angle at point B. On that corner, the newly poured foundation for a building takes the shape of a parallelogram. Which diagonal, AC- or BD-, is longer?42E 43E Prove: In a parallelogram, the sum of the squares of the lengths of its diagonals is equal to the sum of the squares of the lengths of its sides.Note: Exercises preceded by an asterisk are of a more challenging nature. a As shown, must quadrilateral ABCD be a parallelogram? b Given the lengths of the sides as shown, is the measure of A unique?a As shown, must RSTV be a parallelogram? b With measures as shown, is it necessary that RS=8?In the drawing, suppose that WY and XZ bisect each other. What type of quadrilateral is WXYZ?In the drawing, suppose that ZX is the perpendicular bisector of WY. What type of quadrilateral is WXYZ?A carpenter lays out boards of lengths 8 ft, 8 ft, 4 ft, and 4 ft by placing them end to end. a If these are joined at the ends to form a quadrilateral that has the 8-ft pieces connected in over, what type of quadrilateral is formed? b If these are joined at the ends to form a quadrilateral that has the 4-ft and 8-ft pieces alternating, what type of quadrilateral is formed?A carpenter joins four boards of lengths 6 ft, 6 ft, 4 ft, and 4 ft, in that order, to form quadrilateral ABCD as shown. a What type of quadrilateral is formed? b How are angles B and D related?In parallelogram ABCD not shown, AB=8, mB=110, and BC=5. Which diagonal has the greater length?In quadrilateral WXYZ, the measures of selected angles are shown. a What type of quadrilateral is WXYZ? b Which diagonal of the quadrilateral has the greater length?In ABC, M and N are midpoints of AC and BC, respectively. If AB=12.36, how long is MN?In ABC, M and N are midpoints of AC and BC, respectively. If MN=7.65, how long is AB?In Exercises 11 to14 , assume that X, Y , and Z are midpoints of the sides of RST. If RS=12, ST=14, and RT=16, find: a XY b XZ c YZ 12E In Exercises 11 to 14, assume that X, Y, and Z are midpoints of the sides of RST. For Exercise 12 to 14, see the figure for Exercise 11. If the perimeter sum of the lengths of all three sides of RST is 20, what is the perimeter of XYZ?14E 15E 16E For compactness, the drop-down wheels of a stretcher or gurney are folded under it as shown. In order for the boards upper surface to be parallel to the ground when the wheels are dropped, what relationship must exist between AB and CD?For compactness, the drop-down legs of an ironing board fold up under the board. A sliding mechanism at point A and the legs being connected at common midpoint M cause the boards upper surface to be parallel to the floor. How are AB and CD related?In Exercises 19 to 24, complete each proof. Given: 12and34 Prove: MNPQ is a kite PROOF Statements Reasons 1. 12and34 1. ? 2. NQNQ 2. ? 3. ? 3. ASA 4. MNPN and MQPQ 4. ? 5. ? 5. If a quadrilateral has two pairs of adjacent sides, it is a kite In Exercises 19 to 24, complete each proof. Given: Quadrilateral ABCD, with midpoints E, F, G, and H of the sides Prove: EFHG PROOF Statements Reasons 1. ? 1. Given 2. Draw AC 2. Through two points, there is one line 3. In ABC, EFAC and in ADC, HGAC 3. ? 4. ? 4. If two lines are to the same line, these lines are to each other In Exercises 19 to24 , complete each proof. Given: M-Q-T and P-Q-R such that MNPQ and QRST are s Prove: NS In Exercise 19 to24, complete each proof. Given: WXYZ with diagonals WY and XZ WMXYMZ Prove:In Exercise 19 to24, complete each proof. Given: Kite HJKL with diagonal HK Prove: HK bisects LHJ In Exercise 19 to24, complete each proof. Given: MNPQ, with T the midpoint of MN and S the midpoint of QP Prove: QMSNPT and MSPT is a 25E In Exercises 25 to 28, write a formal proof of each theorem or corollary. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.27E 28E In Exercises 29 to 31, M and Nare the midpoints of sides RS and RT ofRST, respectively. Given:MN=2y-3 ST=3y Find:y, MN, and ST In Exercises 29 to 31, M and Nare the midpoints of sides RS and RT ofRST, respectively. Given: MN=x2+5 ST=x2x+5 Find: x, MN, ST In Exercises 29 to 31, M and Nare the midpoints of sides RS and RT ofRST, respectively. Given: RM=RN=2x+1 ST=5x-3 mR=60 Find: x, RM, and ST 32E For Exercises 32 to 35, consider kite ABCD with ABAD andBCDC. For kite ABCD, mC=m-30 while mA=mB-50. Find mB.For Exercises 32 to 35, consider kite ABCD with ABAD andBCDC. For kite ABCD, AB=BC+5. If the perimeter of ABCD is 59.2, find BC.For Exercises 32 to 35, consider kite ABCD with ABAD andBCDC. For kite ABCD, AB=x6+5, AD=x3+3, and BC=x-2. Find the perimeter of ABCD.RSTV is a kite, with RSST and RVVT. If mSTV=40, how large is the angle formed a by the bisectors of RST and STV? b by the bisectors of SRV and RST?In concave kite ABCD, there is an interior angle at vertex B that is a reflex angle. Given that mA=mC=mD=30, find the measure of the indicated reflex angle.If the length of side AB for kite ABCD is 6 in., find the length of AC not shown. Recall that mA=mC=mD=30.Prove that the segment that joins the midpoints of two sides of a triangle has a length equal to one-half the length of the third side. HINT: In the drawing, MN is extended to D , a point on CD . Also, CD is a parallel to AB .Prove that when the midpoints of consecutive sides of a quadrilateral are joined in order, the resulting quadrilateral is a parallelogram.Being as specific as possible, name the type of quadrilateral that ahas four congruent sides. bis a parallelogram with a right angle.Being as specific as possible, name the type of quadrilateral that ahas two pairs of congruent adjacent sides. bhas two pairs of congruent opposite sides.Being as specific as possible, name the type of parallelogram that ahas congruent diagonals. bhas perpendicular diagonals.Being as specific as possible, name the type of rhombus that ahas all angles congruent. bhas congruent diagonals.If the diagonals of a parallelogram are perpendicular and congruent, what can you conclude regarding the parallelogram?If the diagonals of a quadrilateral are perpendicular bisectors of each other but not congruent, what can you conclude regarding the quadrilateral?A line segment joins the midpoints of two opposite sides of a rectangle as shown. What can you conclude regarding MNandMN?In Exercises 8 to 10, use the properties of rectangles to solve each problem. Rectangle ABCD is shown in the figure. Exercises 8 - 10 Given: AB = 5 and BC = 12 Find: CD, AD, and AC not shown 9E In Exercises 8 to 10, use the properties of rectangles to solve each problem. Rectangle ABCD is shown in the figure. In Exercise 9 and 10, see the figure for Exercise 8. Exercises 8 10 Given: AB = x y and BC = x 2y, and CD = 2x y 1, and DA = 3x 3y 1 Find: x and y In Exercises 11 to 14, consider MNPQ with diagonals MPandNQ. When the answer is not a whole number, leave a square root answer. Exercises 11 14 If MQ = 6 and MN = 8, find NQ and MP.In Exercises 11 to 14, consider MNPQ with diagonals MPandNQ. When the answer is not a whole number, leave a square root answer. Exercises 11 14 If QP = 9 and NP = 6, find NQ and MP.In Exercises 11 to 14, consider MNPQ with diagonals MPandNQ. When the answer is not a whole number, leave a square root answer. Exercises 11 14 If NP = 7 and MP = 11, find QP and MN.In Exercises 11 to 14, consider MNPQ with diagonals MPandNQ. When the answer is not a whole number, leave a square root answer. Exercises 11 14 If QP = 15 and MP = 17, find MQ and NP.In Exercises 15 to 18, consider rhombus ABCD with diagonals ACandDB. When the answer is not a whole number, leave a square root answer. Exercises 15 18 If AE = 5 and DE = 4, find AD.In Exercises 15 to 18, consider rhombus ABCD with diagonals ACandDB. When the answer is not a whole number, leave a square root answer. Exercises 15 18 If AE = 6 and EB = 5, find AB.In Exercises 15 to 18, consider rhombus ABCD with diagonals ACandDB. When the answer is not a whole number, leave a square root answer. Exercises 15 18 If AC = 10 and DB = 6, find AD.In Exercises 15 to 18, consider rhombus ABCD with diagonals ACandDB. When the answer is not a whole number, leave a square root answer. Exercises 15 18 If AC = 14 and DB = 10, find BC.Given: ABCD not shown with AB = 8 and BC = 6; M and N are the midpoints of sides ABandBC, respectively. Find: MN Given: Rhombus RSTV not shown with diagonals RTandSV so that RT = 8 and SV = 6 Find: RS, the length of a side 21E 22E 23E 24E 25E Which types of quadrilaterals is are necessarily cyclic? a A kite b A rectangle Find the perimeter of the cyclic quadrilateral shown.Find the perimeter of the square shown.29E 30E 31E 32E 33E 34E 35E 36E In Exercises 32 to 37, write a formal proof of each theorem. If the midpoints of the sides of a rectangle are joined in order, the quadrilateral formed is a rhombus.38E 39E a Argue that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices of the triangle. Use the fact that the congruent diagonals of a rectangle bisect each other. Be sure to provide a drawing. bUse the relationship from part a to find CM, the length of the median to the hypotenuse of right ABC, in which mC=90, AC = 6, and BC = 8.Two sets of rails railroad tracks are equally spaced intersect but not at right angles. Being as specific as possible, indicate what type of quadrilateral WXYZ is formed.In square ABCD not shown, point E lies on side DC. If AB=8 and AE=10, find BE.In square ABCD not shown, point E lies in the interior of ABCD in such a way that ABE is an equilateral triangle. Find mDEC.The sides of square ABCD are trisected at the indicated points. If AB = 3, find the perimeter of a quadrilateral EGIK. b quadrilateral EHIL.Find the measures of the remaining angles of trapezoid ABCD not shown if ABDC and mA=58 and mC=125.Find the measures of the remaining angles of trapezoid ABCD not shown if ABDC and mB=63 and mD=118.What type of trapezoid a has congruent diagonals. b has congruent base angles.What type quadrilateral is formed when the midpoints of the sides of an isosceles trapezoid are joined in order.Given isosceles trapezoid ABCD, Find. a AC, if BD = 12.3 cm b x, AC=3(x+7) and BD=9(x6).In trapezoid ABCD, MN is the median. Without writing a formal proof explain why MN=12(AB+DC).If HandJ are supplementary, what type of quadrilateral is HJKL.If HandJ are supplementary in HJKL, are KandL necessarily supplementary also?For Exercises 9 and 10, consider isosceles trapezoid RSTV with RSVT , and midpoints M, N, P, and Q of the sides. Would RSTV have symmetry with respect to a MP? b QN? Exercises 9, 10 For Exercises 9 and 10, consider isosceles trapezoid RSTV with RSVT, and midpoints M, N, P, Q of the sides. a Does QN=12(RS+VT)? b Does MP=12(RV+ST)? Exercises 9, 10 In Exercises 11 to 16, the drawing shows trapezoid ABCD with ABDC ; also, M and N are midpoints of AD and BC , respectively. Exercises 11-16 Given: AB=7.3andDC=12.1 Find: MN In Exercises 11 to 16, the drawing shows trapezoid ABCD with ABDC ; also, M and N are midpoints of AD and BC , respectively. Exercises 11-16 Given: MN=6.3andDC=7.5 Find: AB In Exercises 11 to 16, the drawing shows trapezoid ABCD with ABDC ; also, M and N are midpoints of AD and BC , respectively. Exercises 11-16 Given: AB=8.2andMN=9.5 Find: DC In Exercises 11 to 16, the drawing shows trapezoid ABCD with ABDC ; also, M and N are midpoints of AD and BC , respectively. Exercises 11-16 Given: AB=7x+5, DC=4x2 and MN=5x+3 Find: x.In Exercises 11 to 16, the drawing shows trapezoid ABCD with ABDC ; also, M and N are midpoints of AD and BC , respectively. Exercises 11-16 Given: AB=6x+5, DC=8x1. Find: MN, in terms of x.In Exercises 11 to 16, the drawing shows trapezoid ABCD with ABDC ; also, M and N are midpoints of AD and BC , respectively. Exercises 11-16 Given: AB=x+3y+4 and DC=3x+5y2. Find: MN, in terms of xandy.Given: ABCD is an isosceles trapezoid. Prove: ABE is isosceles. Exercises 17, 18 Given: Isosceles ABE with AEBE; also, D and C are midpoints of AE and BE, respectively. Prove: ABCD is an isosceles trapezoid. Exercises 17, 18 In isosceles trapezoid WXYZ with bases ZY and WX, ZY = 8, YX = 10 and WX = 20. Find height h the length of ZD or YE. Exercises 19, 20 In trapezoid WXYZ with bases ZY and WX, ZY = 12, YX = 10, WZ = 17, and ZD = 8. Find the length of base WX. Exercises 19, 20 In isosceles trapezoid MNPQ with MNQP, diagonal MPMQ. If PQ = 13 and NP = 5, how long is diagonal MP?In trapezoid RSTV, RVST,mSRV=90, and M and N are midpoints of the nonparallel sides. a What type of triangle is RMN? b If ST = 13, RV = 17 and RS = 16, How long is RN? c What type of triangle is RVN? Hint: Use lengths of sides found in part b.Each vertical section of a suspension bridge is in the shape of a trapezoid. For additional support, a vertical cable is placed midway as shown. If the two vertical columns shown have heights of 20 ft and 24 ft and the section is 10 ft wide. What will the height of the cable be?The state of Nevada approximates the shape of a trapezoid with these dimensions for boundaries: 340 miles on the north, 515 miles on the east, 435 miles on the south and 225 miles on the west. If A and B are points located midway across the north and south boundaries, what is the approximate distance from A to B?In the figure, abc and B is the midpoint of AC. If AB=2x+3, BC=x+7 and DE=3x+2, Find the length of EF. Exercises 25, 26 In the figure, abc and B is the midpoint of AC. If AB=2x+3y, BC=x+y+7 and DE=2x+3y+3 and EF=5xy+2, Find xandy. Exercises 25, 26 27E In exercises 27 to 33, complete a formal proof. The median of a trapezoid is parallel to each base.29E 30E In exercises 27 to 33, complete a formal proof. If three parallel lines intercept congruent segments on one transversal, then they intercept congruent segments on any transversal.32E In exercises 27 to 33, complete a formal proof. Given:EF is the median of trapezoid ABCD. Prove: EF=12(AB+DC). HINT: Using theorem 4.4.7, show that M is the midpoint of AC. For ADCandCBAapply theorem 4.2.5 34E For exercises 34 and 35, EFis the median of trapezoid ABCD in the figure above. Suppose that EM=7.1andMF=3.5 Find: a AB b EF c DC d Whether EF=12(AB+DC)Given: ABDC mA=mB=56CEDA and CF bisects DCB Find: mFCE 37E 38E The vertical side wall of an in-ground pool that is 24 ft in length has the shape of a right trapezoid. What is the depth of the pool in the middle?40E With MNQP and MQQP, MNPQ is a right trapezoid. Find a mP, if mMNPmM=31. b the length of NR, if MN = 6 in., NP = 5 in., and QP = 9 in. Exercises 43, 44 With MNQP and MQ, MNPQ is a right trapezoid. Find a mP, if mMNPmP=54 b the length of the side NP, if MN = 15 cm, MQ = 12 cm, and PQ = 20 cm. Exercises 43, 44 43E 44E Draw and then trisect AB. Use the construction method found in example 7.Review Exercises State whether the statements in Review Exercises 1 to 12 are always true A, sometimes true S, or never true N. A square is a rectangle.2CR 3CR 4CR 5CR 6CR 7CR Review Exercises State whether the statements in Review Exercises 1 to 12 are always true A, sometimes true S, or never true N. Opposite angles of a rhombus are congruent.9CR 10CR 11CR 12CR Review Exercises Given: ABCD CD=2x+3 BC=5x-4 Perimeter of ABCD=96 cm Find: The lengths of the sides of ABCD Review Exercises Given: ABCD mA=2x+6 mB=x+24 Find: mC Review Exercises The diagonals of ABCD not shown are perpendicular. If one diagonal has a length of 10 and the other diagonal has a length of 24, find the perimeter of the parallelogram.Review Exercises Given: MNOP mM=4x mO=2x+50 Find: mMandmP Review Exercises Using the information from Review Exercise 16, determine which diagonal MO- or PN- would be longer. Exercise 16: Given: MNOP mM=4x mO=2x+50 Find: mMandmP Review Exercises In quadrilateral ABCD, M is the midpoint only of BD- and AC-DB- at M. What special type of quadrilateral is ABCD?Review Exercises In isosceles trapezoid DEFG, DE-GF- and mD=108. Find the measures of the other angles in the trapezoid.One base of a trapezoid has a length of 12.3 cm and the length of the other base is 17.5 cm. Find the length of the median of the trapezoid.Review Exercises In trapezoid MNOP, MN-PO- and R and S are the mid-points of MP- and NO- respectively. Find the lengths of the bases if RS=15, MN=3x+2, and PO=2x-7.Review Exercises In Review Exercises 22 to 24, M and N are the midpoints of FJ- and FH- respectively. Given: Isosceles FJH with FJ-FH- FM=2y+3 NH=5y-9 JH=2y Find: The perimeter of FMN Review Exercises In Review Exercises 22 to 24, M and N are the midpoints of FJ- and FH- respectively. Given: JH=12 mJ=80 mF=60 Prove: MN,mFMN,mFNM Review Exercises In Review Exercises 22 to 24, M and N are the midpoints of FJ- and FH- respectively. Given: MN=x2+6 JH=2xx+2 Prove: x,MN,JH Review Exercises Given: ABCD is a AF-CE- Prove: DF-EB-Review Exercises Given: ABEF is a rectangle BCDE is a rectangle FE-=ED- Prove: AE-BD- andAE-BD-27CR 28CR Review Exercises Given: ABCD is a parallelogram DC-BN- 34 Prove: ABCD is a rhombus Review Exercises Given: TWX is an isosceles, with base WX- RY-WX- Prove: RWXY is an isoscels trapezoid 31CR Review Exercises Draw rectangle ABCD with AB=5 and BC=12. Include diagonals AC- and BD-. a How are AB- and BC- related? b Find the length of diagonal AC-.Review Exercises Draw rectangle WXYZ with diagonals WY- and XZ-. Let WY- name the longer diagonal. a How are diagonals WY- and XZ- related? b If WX=17 and XZ=16, find the length of diagonal WY-.34CR Review Exercises What type of quadrilateral is formed when the triangle is reflected across the indicated side? a Isosceles ABC across BC- b Obtuse XYZ across XY-Consider ABCD as shown. a How are A and C related? b How are A and B related?In RSTV not shown, RS=5.3 cm and ST=4.1 cm. Find the perimeter of RSTV.3CT 4CT 5CT Complete each statement: a If a quadrilateral has two pair of congruent adjacent sides, then the quadrilateral is an________. b If a quadrilateral has two pair of congruent opposite sides, then the quadrilateral is an________.7CT 8CT 9CT In ABC, M is the midpoint of AB and N is the midpoint of AC. If MN= 3x-11 and BC= 4x24, find the value of x._In rectangle ABCD, AD=12 and DC=5. Find the length of diagonal AC not shown. _In trapezoid RSTV, RSVT. a Which sides are the legs of RSTV?_ b Name two angles that are supplementary. _In trapezoid RSTV, RSVT and MN is the median, Find the length MN if RS=12.4 in. and VT=16.2 in. _In trapezoid RSTV of Exercise 13, RSVT and MN is the median, Find x if VT=2x+9,MN=6x13,andRS=15. _ Exercise 13, 14 Complete the proof of the following theorem: In a kite, one pair of opposite angles are congruent. Given: Kite ABCD; ABADandBCDC Prove: BD PROOF Statements Reasons 1_________ 2. Draw AC 3.__________ 4. ACDACB 5.__________ 1.______________ 2. Through two points, there is exactly one line. 3. Identity 4.____________ 5._________________Complete the proof of the following theorem: The diagonals of an isosceles trapezoid are congruent. Given: Trapezoid ABCD; ABDC and ADBC. Prove: ACBD PROOF Statements Reasons 1_________ 2. ADCBCD 3. DCDC 4. ADCBCD 5.__________ 1.______________ 2. Base s of an isosceles trapezoid are _______. 3._________ 4.____________ 5. CPCTC In Kite RSTV, RS=2x4,ST=x1,TV=y3andRV=y. Find the perimeter of RSTV.In Exercises 1 to 4, give the ratios in simplified form. a 12 to 15 c 1 ft to 18 in. b 12 in. to 15 in. d 1 ft to 18 oz In Exercises 1 to 4, give the ratios in simplified form. a 20 to 36 c 20 oz to 2 lb 1 lb = 16 oz b 24 oz to 52 oz d 2 lb to 20 oz In Exercises 1 to 4, give the ratios in simplified form. a 15:24 c 2 m:150 cm 1 m = 100 cm b 2 ft:2 yd 1 yd = 3 ft d 2 m:1 lb In Exercises 1 to 4, give the ratios in simplified form. a 24:32 c 150 cm:2 m b 12 in.:2 yd d 1 gal:24 mi In Exercises 5 to 14, find the value of x in each proportion. a x4=912 b 7x=2124 In Exercises 5 to 14, find the value of x in each proportion. a x110=35 b x+16=1012 In Exercises 5 to 14, find the value of x in each proportion. a x38=x+324 b x+16=4x118 In Exercises 5 to 14, find the value of x in each proportion. a 9x=x16 b 32x=x2 In Exercises 5 to 14, find the value of x in each proportion. a x4=7x b x6=3x In Exercises 5 to 14, find the value of x in each proportion. a x+13=10x+2 b x25=12x+2 In Exercises 5 to 14, find the value of x in each proportion. a x+1x=102x b 2x+1x+1=143x1 In Exercises 5 to 14, find the value of x in each proportion. a x+12=7x1 b x+13=5x2 In Exercises 5 to 14, find the value of x in each proportion. a x+1x=2x3 b x+1x1=2x5 In Exercises 5 to 14, find the value of x in each proportion. a x+1x=xx1 b x+2x=2xx2 Sarah ran the 300-m hurdles in 47.7 sec. In meters per second, find the rate at which Sarah ran. Give the answer to the nearest tenth of a meter per second.Fran has been hired to sew the dance troupes dresses for the school musical. If 1313 yd of material is needed for the four dresses, find the rate that describes the amount of material needed for each dress.In Exercises 17 to 22, use proportions to solve each problem. A recipe calls for 4 eggs and 3 cups of milk. To prepare for a larger number of guests, a cook uses 14 eggs. How many cups of milk are needed?18E In Exercises 17 to 22, use proportions to solve each problem. An electrician installs 25 electrical outlets in a new six room house. Assuming proportionality, how many outlets should be installed in a new construction having seven rooms? Round to nearest integer.In Exercises 17 to 22, use proportions to solve each problem. The secretarial pool 15 secretaries in all on one floor of a corporate complex has access to four copy machines. If there are 23 secretaries on a different floor, approximately what number of copy machines should be available? Assume a proportionality.In Exercises 17 to 22, use proportions to solve each problem. Assume that AD is the geometric mean of BD and DC in ABC shown in the accompanying drawing. a Find AD if BD = 6 and DC = 8. b Find BD if AD = 6 and DC = 8.22E The salaries of a secretary, a salesperson, and a vice president for a retail sales company are in the ratio 2:3:5. If their combined annual salaries amount to 124, 500, what is the annual salary of each?The salaries of a school cook, custodian, and bus driver are in the ratio 2:4:3. If their combined monthly salaries for November total 8, 280, what is the monthly salary for each person?If the measures of the angles of a quadrilateral are in the ratio of 3:4:5:6, find the measure of each angle.If the measures of the angles of a quadrilateral are in the ratio of 2:3:4:6, find the measure of each angle.27E 28E If 1 in. equals 2.54 cm, use a proportion to convert 12 in. to centimeters. (HINT:2.54cm1in.=xcm12in.)If 1 kg equals 2.2 lb, use a proportion to convert 12 pounds to kilograms.For the quadrilaterals shown, MNWX=NPXY=PQYZ=MQWZ. If MN = 7, WX = 3, and PQ = 6, to find YZ.32E Two numbers a and b are in the ratio 3:4. If the first number is decreased by 2 and the second is decreased by 1, they are in the ratio 2:3. Find a and b.Two numbers a and b are in the ratio 2:3. If both numbers are decreased by 2, the ratio of the resulting numbers becomes 3:5. Find a and b.If the ratio of the measure of the complement of an angle to the measure of its supplement is 1:3, find the measure of the angle.If the ratio of the measure of the complement of an angle to the measure of its supplement is 1:4, find the measure of the angle.On a blueprint, a 1-in. scale corresponds to 3 ft. To show a room with actual dimensions 12 ft wide by 14 ft long, what dimensions should be shown on the blueprint?38E Find a the exact length of an ideal rectangle with width W = 5 by solving 5L=L55. b the approximate length of an ideal rectangle with width W = 5 by using L1.62W Prove: If ab=cd where a, b, c and d are nonzero, then ac=bd.41E

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