Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Chapter 4.CR, Problem 2CR
To determine
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Whether the provided statement is always true (A), sometimes true (S) or never true (N).
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Chapter 4 Solutions
Elementary Geometry For College Students, 7e
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 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 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 - Prob. 31ECh. 4.1 - In Exercises 31 to 34, write a formal proof of...Ch. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 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 - Prob. 39ECh. 4.1 - In quadrilaterals ABCD and EFGH, AB-DC-, EF-HG-,...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 - Prob. 44ECh. 4.1 - Prob. 45ECh. 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 - Prob. 13ECh. 4.2 - In Exercises 11 to 14, assume that X, Y, and Z are...Ch. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 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 - Prob. 25ECh. 4.2 - In Exercises 25 to 28, write a formal proof of...Ch. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 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 - Prob. 32ECh. 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 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - For regular octagon ABCDEFGH, a are quadrilateral...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 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - For Exercises 21 t 24, let...Ch. 4.3 - In Exercises 25 and 26, supply the missing...Ch. 4.3 - In Exercises 25 and 26, supply the missing...Ch. 4.3 - Prob. 27ECh. 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 - Are quadrilaterals ABCD and EFGH congruent aif...Ch. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - In Exercises 34 to 39, write a formal proof of...Ch. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - In Exercises 34 to 39, write a formal proof of...Ch. 4.3 - Prob. 40ECh. 4.3 - In Exercises 40 to 41, 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 a 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 - Prob. 27ECh. 4.4 - HJKL and WXYZ are right trapezoids. Are these...Ch. 4.4 - In exercises 29 to 35, complete a formal proof....Ch. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - In exercises 29 to 35, complete a formal proof. If...Ch. 4.4 - Prob. 34ECh. 4.4 - Prob. 35ECh. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Given: ABDC mA=mB=56CEDA and CF bisects DCB Find:...Ch. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - The vertical side wall of an in-ground pool that...Ch. 4.4 - Prob. 42ECh. 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 trapezoid ABCD not shown, mA=x2+10, mB=x3+50...Ch. 4.4 - Prob. 46ECh. 4.4 - Draw and then trisect AB. Use the construction...Ch. 4.4 - Prob. 48ECh. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Prob. 2CRCh. 4.CR - Prob. 3CRCh. 4.CR - Prob. 4CRCh. 4.CR - Prob. 5CRCh. 4.CR - Prob. 6CRCh. 4.CR - Prob. 7CRCh. 4.CR - Review Exercises State whether the statements in...Ch. 4.CR - Prob. 9CRCh. 4.CR - Prob. 10CRCh. 4.CR - Prob. 11CRCh. 4.CR - Prob. 12CRCh. 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 - Prob. 27CRCh. 4.CR - Prob. 28CRCh. 4.CR - Review Exercises Given: ABCD is a parallelogram...Ch. 4.CR - Review Exercises Given: TWX is an isosceles, with...Ch. 4.CR - Prob. 31CRCh. 4.CR - Review Exercises Draw rectangle ABCD with AB=5 and...Ch. 4.CR - Review Exercises Draw rectangle WXYZ with...Ch. 4.CR - Prob. 34CRCh. 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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- 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.arrow_forwardClassify as true or false: a If the vertex angles of two isosceles triangles are congruent, the triangles are similar. b Any two equilateral triangles are similar.arrow_forwardA carpenter has placed a square over an angle in such a manner that ABAC and BDCD. In the drawing, what can you conclude about the location of point D?arrow_forward
- In trapezoid RSTV, RSVT. a Which sides are the legs of RSTV? b Name two angles that are supplementary.arrow_forwardFor a given triangle such as ABC, what word describes the point of concurrency for athe three perpendicular bisectors of sides? _____________ bthe three altitudes? ____________________arrow_forwarda 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.arrow_forward
- 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?arrow_forwardIn 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._arrow_forwardWhen 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?arrow_forward
- 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.arrow_forwardState whether the sentences in Review Exercises 33 to 37 are always true A, sometimes true S, or never true N. The supplement of an obtuse angle is another obtuse angle.arrow_forwardTwo 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?arrow_forward
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