Math

GeometryElementary Geometry for College Studentsa) 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. b) Use the relationship from part a) to find CM , the length of the median to the hypotenuse of right △ A B C , in which m ∠ C = 90 ∘ , AC = 6, and BC = 8.BuyFind*launch*

6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

Chapter 4.3, Problem 40E

Textbook Problem

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.

b) Use the relationship from part a) to find *CM*, the length of the median to the hypotenuse of right
*AC* = 6, and *BC* = 8.

Elementary Geometry for College Students

Ch. 4.1 - ABCD is a parallelogram. a Using a ruler, compare...Ch. 4.1 - ABCD is a parallelogram. a Using a ruler, compare...Ch. 4.1 - MNPQ is a parallelogram. Suppose that MQ=5, MN=8,...Ch. 4.1 - MNPQ is a parallelogram. Suppose that MQ=12.7,...Ch. 4.1 - For Exercises 5 to 8, MNPQ is a parallelogram with...Ch. 4.1 - For Exercises 5 to 8, MNPQ is a parallelogram with...Ch. 4.1 - For Exercises 5 to 8, MNPQ is a parallelogram with...Ch. 4.1 - For Exercises 5 to 8, MNPQ is a parallelogram with...Ch. 4.1 - Given that AB=3x+2, BC=4x+1, and CD=5x-2, find the...Ch. 4.1 - Given that mA=2x+3, and mC=3x-27, find the measure...

Ch. 4.1 - Given that mA=2x+3, and mB=3x-23, find the measure...Ch. 4.1 - Given that mA=2x5, and mB=x2, find the measure of...Ch. 4.1 - Given that mA=2x3, and mC=x2+20, find the measure...Ch. 4.1 - Given that mA=2x+y, mB=2x+3y-20, and mC=3x-y+16,...Ch. 4.1 - Assuming that mBmA in , which diagonal AC-orBD-...Ch. 4.1 - Suppose that diagonals AC-andBD- of are drawn and...Ch. 4.1 - In Exercises 17 and 18, consider with VX- RS- and...Ch. 4.1 - In Exercises 17 and 18, consider with VX- RS- and...Ch. 4.1 - In Exercises 19 to 22, classify each statement as...Ch. 4.1 - In Exercises 19 to 22, classify each statement as...Ch. 4.1 - In Exercises 19 to 22, classify each statement as...Ch. 4.1 - In Exercises 19 to 22, classify each statement as...Ch. 4.1 - In quadrilateral RSTV, the midpoints of...Ch. 4.1 - In quadrilateral ABCD, the midpoints of opposite...Ch. 4.1 - Quadrilateral ABCD has AB-DC- and AD-BC-. Using...Ch. 4.1 - Quadrilateral RSTV has RS-TV- and RS-TV-. Using...Ch. 4.1 - In Exercises 27-30, use the definition of a...Ch. 4.1 - In Exercises 27-30, use the definition of a...Ch. 4.1 - In Exercises 27 to 30, use the definition of a...Ch. 4.1 - In Exercises 27-30, use the definition of a...Ch. 4.1 - In Exercises 31 to 34, write a formal proof of...Ch. 4.1 - In Exercises 31 to 34, write a formal proof of...Ch. 4.1 - In Exercises 31 to 34, write a formal proof of...Ch. 4.1 - In Exercises 31 to 34, write a formal proof of...Ch. 4.1 - The bisectors of two consecutive angles of HJKL...Ch. 4.1 - When the bisectors of two consecutive angles of a...Ch. 4.1 - Draw parallelogram RSTV with mR=700 and mS=1100....Ch. 4.1 - Draw parallelogram RSTV so that the diagonals have...Ch. 4.1 - The following problem is based on the...Ch. 4.1 - In the drawing for Exercise 41, the bearing...Ch. 4.1 - Two streets meet to form an obtuse angle at point...Ch. 4.1 - To test the accuracy of the foundations...Ch. 4.1 - For a quadrilateral ABCD, the measures of its...Ch. 4.1 - Prove: In a parallelogram, the sum of the squares...Ch. 4.2 - Note: Exercises preceded by an asterisk are of a...Ch. 4.2 - a As shown, must RSTV be a parallelogram? b With...Ch. 4.2 - In the drawing, suppose that WY and XZ bisect each...Ch. 4.2 - In the drawing, suppose that ZX is the...Ch. 4.2 - A carpenter lays out boards of lengths 8 ft, 8 ft,...Ch. 4.2 - A carpenter joins four boards of lengths 6 ft, 6...Ch. 4.2 - In parallelogram ABCD not shown, AB=8, mB=110, and...Ch. 4.2 - In quadrilateral WXYZ, the measures of selected...Ch. 4.2 - In ABC, M and N are midpoints of AC and BC,...Ch. 4.2 - In ABC, M and N are midpoints of AC and BC,...Ch. 4.2 - In Exercises 11 to14 , assume that X, Y , and Z...Ch. 4.2 - In Exercises 11 to 14, assume that X, Y, and Z are...Ch. 4.2 - In Exercises 11 to 14, assume that X, Y, and Z are...Ch. 4.2 - In Exercises 11 to 14, assume that X, Y, and Z are...Ch. 4.2 - Consider and kite. a Does it have line symmetry?...Ch. 4.2 - Consider any parallelogram. a Does it have line...Ch. 4.2 - For compactness, the drop-down wheels of a...Ch. 4.2 - For compactness, the drop-down legs of an ironing...Ch. 4.2 - In Exercises 19 to 24, complete each proof. Given:...Ch. 4.2 - In Exercises 19 to 24, complete each proof. Given:...Ch. 4.2 - In Exercises 19 to24 , complete each proof. Given:...Ch. 4.2 - In Exercise 19 to24, complete each proof. Given:...Ch. 4.2 - In Exercise 19 to24, complete each proof. Given:...Ch. 4.2 - In Exercise 19 to24, complete each proof. Given:...Ch. 4.2 - In Exercises 25 to 28, write a formal proof of...Ch. 4.2 - In Exercises 25 to 28, write a formal proof of...Ch. 4.2 - In Exercises 25 to 28, write a formal proof of...Ch. 4.2 - In Exercises 25 to 28, write a formal proof of...Ch. 4.2 - In Exercises 29 to 31, M and Nare the midpoints of...Ch. 4.2 - In Exercises 29 to 31, M and Nare the midpoints of...Ch. 4.2 - In Exercises 29 to 31, M and Nare the midpoints of...Ch. 4.2 - For Exercises 32 to 35, consider kite ABCD with...Ch. 4.2 - For Exercises 32 to 35, consider kite ABCD with...Ch. 4.2 - For Exercises 32 to 35, consider kite ABCD with...Ch. 4.2 - For Exercises 32 to 35, consider kite ABCD with...Ch. 4.2 - RSTV is a kite, with RSST and RVVT. If mSTV=40,...Ch. 4.2 - In concave kite ABCD, there is an interior angle...Ch. 4.2 - If the length of side AB for kite ABCD is 6 in.,...Ch. 4.2 - Prove that the segment that joins the midpoints of...Ch. 4.2 - Prove that when the midpoints of consecutive sides...Ch. 4.3 - Being as specific as possible, name the type of...Ch. 4.3 - Being as specific as possible, name the type of...Ch. 4.3 - Being as specific as possible, name the type of...Ch. 4.3 - Being as specific as possible, name the type of...Ch. 4.3 - If the diagonals of a parallelogram are...Ch. 4.3 - If the diagonals of a quadrilateral are...Ch. 4.3 - A line segment joins the midpoints of two opposite...Ch. 4.3 - In Exercises 8 to 10, use the properties of...Ch. 4.3 - In Exercises 8 to 10, use the properties of...Ch. 4.3 - In Exercises 8 to 10, use the properties of...Ch. 4.3 - In Exercises 11 to 14, consider MNPQ with...Ch. 4.3 - In Exercises 11 to 14, consider MNPQ with...Ch. 4.3 - In Exercises 11 to 14, consider MNPQ with...Ch. 4.3 - In Exercises 11 to 14, consider MNPQ with...Ch. 4.3 - In Exercises 15 to 18, consider rhombus ABCD with...Ch. 4.3 - In Exercises 15 to 18, consider rhombus ABCD with...Ch. 4.3 - In Exercises 15 to 18, consider rhombus ABCD with...Ch. 4.3 - In Exercises 15 to 18, consider rhombus ABCD with...Ch. 4.3 - Given: ABCD not shown with AB = 8 and BC = 6; M...Ch. 4.3 - Given: Rhombus RSTV not shown with diagonals...Ch. 4.3 - For Exercises 21 and 22,...Ch. 4.3 - For Exercises 21 and 22,...Ch. 4.3 - In Exercises 23 and 24, supply the missing...Ch. 4.3 - In Exercises 23 and 24, supply the missing...Ch. 4.3 - Which types of quadrilaterals is are necessarily...Ch. 4.3 - Which types of quadrilaterals is are necessarily...Ch. 4.3 - Find the perimeter of the cyclic quadrilateral...Ch. 4.3 - Find the perimeter of the square shown.Ch. 4.3 - In Exercises 29 to 31, explain why each statement...Ch. 4.3 - In Exercises 29 to 31, explain why each statement...Ch. 4.3 - In Exercise 29 to 31, explain why each statement...Ch. 4.3 - In Exercises 32 to 37, write a formal proof of...Ch. 4.3 - In Exercises 32 to 37, write a formal proof of...Ch. 4.3 - In Exercises 32 to 37, write a formal proof of...Ch. 4.3 - In Exercises 32 to 37, write a formal proof of...Ch. 4.3 - In Exercises 32 to 37, write a formal proof of...Ch. 4.3 - In Exercises 32 to 37, write a formal proof of...Ch. 4.3 - In Exercises 38 and 39, you will need to use the...Ch. 4.3 - In Exercises 38 and 39, you will need to use the...Ch. 4.3 - a Argue that the midpoint of the hypotenuse of a...Ch. 4.3 - Two sets of rails railroad tracks are equally...Ch. 4.3 - In square ABCD not shown, point E lies on side DC....Ch. 4.3 - In square ABCD not shown, point E lies in the...Ch. 4.3 - The sides of square ABCD are trisected at the...Ch. 4.4 - Find the measures of the remaining angles of...Ch. 4.4 - Find the measures of the remaining angles of...Ch. 4.4 - What type of trapezoid a has congruent diagonals....Ch. 4.4 - What type quadrilateral is formed when the...Ch. 4.4 - Given isosceles trapezoid ABCD, Find. a AC, if BD...Ch. 4.4 - In trapezoid ABCD, MN is the median. Without...Ch. 4.4 - If HandJ are supplementary, what type of...Ch. 4.4 - If HandJ are supplementary in HJKL, are KandL...Ch. 4.4 - For Exercises 9 and 10, consider isosceles...Ch. 4.4 - For Exercises 9 and 10, consider isosceles...Ch. 4.4 - In Exercises 11 to 16, the drawing shows trapezoid...Ch. 4.4 - In Exercises 11 to 16, the drawing shows trapezoid...Ch. 4.4 - In Exercises 11 to 16, the drawing shows trapezoid...Ch. 4.4 - In Exercises 11 to 16, the drawing shows trapezoid...Ch. 4.4 - In Exercises 11 to 16, the drawing shows trapezoid...Ch. 4.4 - In Exercises 11 to 16, the drawing shows trapezoid...Ch. 4.4 - Given: ABCD is an isosceles trapezoid. Prove: ABE...Ch. 4.4 - Given: Isosceles ABE with AEBE; also, D and C are...Ch. 4.4 - In isosceles trapezoid WXYZ with bases ZY and WX,...Ch. 4.4 - In trapezoid WXYZ with bases ZY and WX, ZY = 12,...Ch. 4.4 - In isosceles trapezoid MNPQ with MNQP, diagonal...Ch. 4.4 - In trapezoid RSTV, RVST,mSRV=90, and M and N are...Ch. 4.4 - Each vertical section of a suspension bridge is in...Ch. 4.4 - The state of Nevada approximates the shape of a...Ch. 4.4 - In the figure, abc and B is the midpoint of AC. If...Ch. 4.4 - In the figure, abc and B is the midpoint of AC. If...Ch. 4.4 - In Exercises 27 to 33, complete a formal proof....Ch. 4.4 - In exercises 27 to 33, complete a formal proof....Ch. 4.4 - In exercises 27 to 33, complete a formal proof. If...Ch. 4.4 - In exercises 27 to 33, complete a formal proof. If...Ch. 4.4 - In exercises 27 to 33, complete a formal proof. If...Ch. 4.4 - In exercises 27 to 33, complete a formal proof. If...Ch. 4.4 - In exercises 27 to 33, complete a formal proof....Ch. 4.4 - For exercises 34 and 35, EFis the median of...Ch. 4.4 - For exercises 34 and 35, EFis the median of...Ch. 4.4 - Given: ABDC mA=mB=56CEDA and CF bisects DCB Find:...Ch. 4.4 - In a gambrel style roof, the gable end of a barn...Ch. 4.4 - Successive steps on a ladder form isosceles...Ch. 4.4 - The vertical side wall of an in-ground pool that...Ch. 4.4 - For the in-ground pool shown in Exercise 41, find...Ch. 4.4 - With MNQP and MQQP, MNPQ is a right trapezoid....Ch. 4.4 - With MNQP and MQ, MNPQ is a right trapezoid. Find...Ch. 4.4 - In trap. ABCD not shown, mA=x2+10, mB=x3+50, and...Ch. 4.4 - In trap. ABCD, BCAB and BCCD. If...Ch. 4.4 - Draw and then trisect AB. Use the construction...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Review Exercises Given: ABCD CD=2x+3 BC=5x-4...Ch. 4.CR - Review Exercises Given: ABCD mA=2x+6 mB=x+24 Find:...Ch. 4.CR - Review Exercises The diagonals of ABCD not shown...Ch. 4.CR - Review Exercises Given: MNOP mM=4x mO=2x+50 Find:...Ch. 4.CR - Review Exercises Using the information from Review...Ch. 4.CR - Review Exercises In quadrilateral ABCD, M is the...Ch. 4.CR - Review Exercises In isosceles trapezoid DEFG,...Ch. 4.CR - One base of a trapezoid has a length of 12.3 cm...Ch. 4.CR - Review Exercises In trapezoid MNOP, MN-PO- and R...Ch. 4.CR - Review Exercises In Review Exercises 22 to 24, M...Ch. 4.CR - Review Exercises In Review Exercises 22 to 24, M...Ch. 4.CR - Review Exercises In Review Exercises 22 to 24, M...Ch. 4.CR - Review Exercises Given: ABCD is a AF-CE- Prove:...Ch. 4.CR - Review Exercises Given: ABEF is a rectangle BCDE...Ch. 4.CR - Review Exercises Given: DE is a median of ADC...Ch. 4.CR - Review Exercises Given: FABHCD EADGCB Prove: ABCD...Ch. 4.CR - Review Exercises Given: ABCD is a parallelogram...Ch. 4.CR - Review Exercises Given: TWX is an isosceles, with...Ch. 4.CR - Review Exercises Construct rhombus ABCD, given...Ch. 4.CR - Review Exercises Draw rectangle ABCD with AB=5 and...Ch. 4.CR - Review Exercises Draw rectangle WXYZ with...Ch. 4.CR - Review Exercises Considering parallelograms,...Ch. 4.CR - Review Exercises What type of quadrilateral is...Ch. 4.CT - Consider ABCD as shown. a How are A and C...Ch. 4.CT - In RSTV not shown, RS=5.3 cm and ST=4.1 cm. Find...Ch. 4.CT - In ABCD, AD=5 and DC=9. If the altitude from...Ch. 4.CT - In RSTV, mS=57. Which diagonal (VSorRT) would have...Ch. 4.CT - In RSTV, VT=3x1,TS=2x+1,andRS=4(x2). Find the...Ch. 4.CT - Complete each statement: a If a quadrilateral has...Ch. 4.CT - Complete each statement: a In RSTV, RW is the...Ch. 4.CT - In ABC, M is the midpoint of AB and N is the...Ch. 4.CT - In ABC, M is the midpoint of AB and N is the...Ch. 4.CT - In ABC, M is the midpoint of AB and N is the...Ch. 4.CT - In rectangle ABCD, AD=12 and DC=5. Find the length...Ch. 4.CT - In trapezoid RSTV, RSVT. a Which sides are the...Ch. 4.CT - In trapezoid RSTV, RSVT and MN is the median, Find...Ch. 4.CT - In trapezoid RSTV of Exercise 13, RSVT and MN is...Ch. 4.CT - Complete the proof of the following theorem: In a...Ch. 4.CT - Complete the proof of the following theorem: The...Ch. 4.CT - In Kite RSTV, RS=2x4,ST=x1,TV=y3andRV=y. Find the...

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