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.

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 △ A B C , in which m ∠ C = 90 ∘ , AC = 6, and BC = 8.

BuyFind

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
Publisher: Cengage Learning
ISBN: 9781285195698
BuyFind

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
Publisher: Cengage Learning
ISBN: 9781285195698

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
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 △ A B C , in which m ∠ C = 90 ∘ , AC = 6, and BC = 8.

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Chapter 4.3,
Problem 39E
Chapter 4.3,
Problem 41E

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Chapter 4 Solutions

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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