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7th Edition

Alexander + 2 others

Publisher: Cengage,

ISBN: 9781337614085

Chapter 2.3, Problem 31E

Textbook Problem

*In Exercises 31 to 33, give a formal proof for each theorem.*

If two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then these lines are parallel.

Elementary Geometry For College Students, 7e

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Ch. 2.1 - For Exercises 1 to 4, lm with transversal v. See...Ch. 2.1 - For Exercises 1 to 4, lm with transversal v. See...Ch. 2.1 - For Exercises 1 to 4, lm with transversal v. See...Ch. 2.1 - For Exercises 1 to 4, lm with transversal v. See...Ch. 2.1 - Use drawings, as needed, to answer each question....Ch. 2.1 - Use drawings, as needed, to answer each question....Ch. 2.1 - Use drawings, as needed, to answer each question....Ch. 2.1 - Use drawings, as needed, to answer each question....Ch. 2.1 - Use drawings, as needed, to answer each question....Ch. 2.1 - Use drawings, as needed, to answer each question....

Ch. 2.1 - Use drawings, as needed, to answer each question....Ch. 2.1 - In Euclidean geometry, how many lines can be drawn...Ch. 2.1 - Lines r and s are cut by the transversal t. Which...Ch. 2.1 - ADBC, ABDC, and mA=92. Find: a mB b mC c mDCh. 2.1 - lm, with transversal t and OQ bisects MNO. If...Ch. 2.1 - Given: lm Transversal t m1=4x+2 m6=4x2 Find: x and...Ch. 2.1 - Given: mn Transversal k m3=x23x m6=(x+4)(x5) Find:...Ch. 2.1 - Given: mn Transversal k m1=5x+y m2=3x+y m8=3x+5y...Ch. 2.1 - Given: mn Transversal k m3=6x+y m5=8x+2y m6=4x+7y...Ch. 2.1 - In the three-dimensional figure, CAAB and BEAB....Ch. 2.1 - Given: lmand34 Prove: 14 See figure below. PROOF...Ch. 2.1 - Given: lmandmn Prove: 14 PROOF Statements Reasons...Ch. 2.1 - Given: CEDF Transversal AB CX bisects ACE DE...Ch. 2.1 - Given: CEDF Transversal AB DE bisects CDF Prove:...Ch. 2.1 - Given: rs Transversal t 1 is a right Prove: 2 is...Ch. 2.1 - Given: ABDEmBAC=42mEDC=54 Find: mACD HINT: There...Ch. 2.1 - Given: ABDEmBAC+mCDE=93 Find: mACD See Hint in...Ch. 2.1 - Given: rs, rt See figure for Exercise 25. Prove:...Ch. 2.1 - In triangle ABC, line t is drawn through vertex A...Ch. 2.1 - In Exercises 30 to 32, write a formal proof of...Ch. 2.1 - In Exercises 30 to 32, write a formal proof of...Ch. 2.1 - In Exercises 30 to 32, write a formal proof of...Ch. 2.1 - Suppose that two lines are cut by a transversal in...Ch. 2.1 - Given: Line l and point P not on l Construct: PQlCh. 2.1 - Given: Triangle ABC with three acute angles....Ch. 2.1 - Given: Triangle MNQ with obtuse MNQ Construct:...Ch. 2.1 - Given: Triangle MNQ with obtuse MNQ Construct:...Ch. 2.1 - Given: A line m and a point T not on m Suppose...Ch. 2.1 - For the figure shown, abc, Find x and y.Ch. 2.2 - Note: Exercises preceded by an asterisk are of a...Ch. 2.2 - Note: Exercises preceded by an asterisk are of a...Ch. 2.2 - Note: Exercises preceded by an asterisk are of a...Ch. 2.2 - Note: Exercises preceded by an asterisk are of a...Ch. 2.2 - In Exercises 5 to 10, draw a conclusion where...Ch. 2.2 - In Exercises 5 to 10, draw a conclusion where...Ch. 2.2 - In Exercises 5 to 10, draw a conclusion where...Ch. 2.2 - In Exercises 5 to 10, draw a conclusion where...Ch. 2.2 - In Exercises 5 to 10, draw a conclusion where...Ch. 2.2 - In Exercises 5 to 10, draw a conclusion where...Ch. 2.2 - Which of the following statements would you prove...Ch. 2.2 - Which of the following statements would you prove...Ch. 2.2 - In Exercises 13 to 16, write the first statement...Ch. 2.2 - In Exercises 13 to 16, write the first statement...Ch. 2.2 - In Exercises 13 to 16, write the first statement...Ch. 2.2 - In Exercises 13 to 16, write the first statement...Ch. 2.2 - For Exercises 17 to 20, the given statement is...Ch. 2.2 - For Exercises 17 to 20, the given statement is...Ch. 2.2 - For Exercises 17 to 20, the given statement is...Ch. 2.2 - For Exercises 17 to 20, the given statement is...Ch. 2.2 - In Exercise 21 and 22, state a conclusion for the...Ch. 2.2 - In Exercise 21 and 22, state a conclusion for the...Ch. 2.2 - A periscope uses an indirect method of...Ch. 2.2 - Some stores use an indirect method of observation....Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.2 - In Exercises 25 to 36, give the indirect proof for...Ch. 2.3 - In Exercises 1 to 6, l and m are cut by...Ch. 2.3 - In Exercises 1 to 6, l and m are cut by...Ch. 2.3 - In Exercises 1 to 6, l and m are cut by...Ch. 2.3 - In Exercises 1 to 6, l and m are cut by...Ch. 2.3 - In Exercises 1 to 6, l and m are cut by...Ch. 2.3 - In Exercises 1 to 6, l and m are cut by...Ch. 2.3 - In Exercise 7 to 16, name the lines if any that...Ch. 2.3 - In Exercise 7 to 16, name the lines if any that...Ch. 2.3 - In Exercise 7 to 16, name the lines if any that...Ch. 2.3 - In Exercise 7 to 16, name the lines if any that...Ch. 2.3 - In Exercise 7 to 16, name the lines if any that...Ch. 2.3 - In Exercise 7 to 16, name the lines if any that...Ch. 2.3 - In Exercise 7 to 16, name the lines if any that...Ch. 2.3 - In Exercise 7 to 16, name the lines if any that...Ch. 2.3 - In Exercise 7 to 16, name the lines if any that...Ch. 2.3 - In Exercise 7 to 16, name the lines if any that...Ch. 2.3 - In Exercise 17 and 18 , complete each proof by...Ch. 2.3 - In Exercises 17 and 18, complete each proof by...Ch. 2.3 - In Exercises 19 to 22, complete the proof. Given:...Ch. 2.3 - In Exercise 19 to 22 complete the proof. Given: 1 ...Ch. 2.3 - In Exercise 19 to 22 complete the proof. Given: DE...Ch. 2.3 - In Exercise 19 to 22 complete the proof. Given: XY...Ch. 2.3 - In Exercise 23 to 30, determine the value of x so...Ch. 2.3 - In Exercise 23 to 30, determine the value of x so...Ch. 2.3 - In Exercise 23 to 30, determine the value of x so...Ch. 2.3 - In Exercise 23 to 30, determine the value of x so...Ch. 2.3 - In Exercise 23 to 30, determine the value of x so...Ch. 2.3 - In Exercise 23 to 30, determine the value of x so...Ch. 2.3 - In Exercise 23 to 30, determine the value of x so...Ch. 2.3 - In Exercise 23 to 30, determine the value of x so...Ch. 2.3 - In Exercises 31 to 33, give a formal proof for...Ch. 2.3 - In Exercises 31 to 33, give a formal proof for...Ch. 2.3 - In Exercises 31 to 33, give a formal proof for...Ch. 2.3 - Explain why the statement in Exercise 33 remains...Ch. 2.3 - Given that point P does not lie on the line l,...Ch. 2.3 - Given that point Q does not lie on AB, construct...Ch. 2.3 - A carpenter drops a plumb line from point A to BC....Ch. 2.3 - Given: m2+m3=90 BE bisects ABC CE bisects BCD...Ch. 2.3 - With angle measures as indicated, determine: a)...Ch. 2.4 - In Exercise 1 to 4, refer to ABC . On the basis of...Ch. 2.4 - In Exercise 1 to 4, refer to ABC . On the basis of...Ch. 2.4 - In Exercise 1 to 4, refer to ABC . On the basis of...Ch. 2.4 - In Exercise 1 to 4, refer to ABC . On the basis of...Ch. 2.4 - Describe the auxiliary line segment as determined,...Ch. 2.4 - Describe the auxiliary line segment as determined,...Ch. 2.4 - In Exercises 7 and 8, classify the trianglenot...Ch. 2.4 - In Exercises 7 and 8, classify the trianglenot...Ch. 2.4 - In Exercises 9 and 10, classify the triangle not...Ch. 2.4 - In Exercises 9 and 10, classify the triangle not...Ch. 2.4 - In Exercises 11 and12, make drawings as needed....Ch. 2.4 - In Exercises 11 and 12, make drawings as needed....Ch. 2.4 - In Exercises 13 to 15, jk and ABC. Given:...Ch. 2.4 - In Exercises 13 to 15, jk and ABC. Given:...Ch. 2.4 - In Exercises 13 to 15, jk and. ABC. Given:...Ch. 2.4 - Given: MNNQ and s as shown Find: x, y, and zCh. 2.4 - Given: ABDC DB bisects ADC mA=110 Find: m3Ch. 2.4 - Given: ABDC DB bisects ADC m1=36 Find: mACh. 2.4 - Given: ABC with BDCE m3=m4=30m1=m2=70 Find: mBCh. 2.4 - Given: ABC with BDCE m1=2xm3=x Find: mB in terms...Ch. 2.4 - Given: ADE with m1=m2=x Find: mDAE=x2 x, m1, and...Ch. 2.4 - Given: ABC with mB=mC=x2 Find: mBAC=x x, mBAC, and...Ch. 2.4 - Consider any triangle and one exterior angle at...Ch. 2.4 - Given: Right ABC with right C m1=7x+4m2=5x+2 Find:...Ch. 2.4 - In Exercises 25 to 27 , see the figure for...Ch. 2.4 - In Exercises 25 to 27 , see the figure for...Ch. 2.4 - In Exercises 25 to 27 , see the figure for...Ch. 2.4 - Given: m1=8(x+2)m3=5x3m5=5(x+1)2 Find: xCh. 2.4 - Given: Find: , , andCh. 2.4 - Given: Equiangular RST Prove: RV bisects SRT RVS...Ch. 2.4 - Given: and intersect Prove: at ;Ch. 2.4 - The sum of the measures of two angles of a...Ch. 2.4 - Draw, if possible, an a isosceles obtuse triangle....Ch. 2.4 - Draw, if possible, a a right scalene triangle. b...Ch. 2.4 - Along a straight shoreline, two houses are located...Ch. 2.4 - An airplane has leveled off is flying horizontally...Ch. 2.4 - On a map, three Los Angeles suburbs are located at...Ch. 2.4 - The roofline of a house shows the shape of a right...Ch. 2.4 - A lamppost has design such that mC=110 and AB....Ch. 2.4 - For the lamppost of Exercise 39, Suppose that...Ch. 2.4 - The triangular symbol on the PLAY button of a DVD...Ch. 2.4 - A polygon with four sides is called quadrilateral....Ch. 2.4 - Explain why the following statement is true. Each...Ch. 2.4 - Explain why the following statement is true. The...Ch. 2.4 - In Exercises 45 to 47, write a formal proof for...Ch. 2.4 - In Exercises 45 to 47, write a formal proof for...Ch. 2.4 - In Exercises 45 to 47, write a formal proof for...Ch. 2.4 - Given: AB, DE and CF ABDE CG bisects BCF FG...Ch. 2.4 - Given: NQ bisects MNP PQ bisects MPR mQ=42 Find:...Ch. 2.4 - Given: In right ABC, AD bisects CAB and BF bisects...Ch. 2.5 - For Exercises 1 and 2, consider a group of regular...Ch. 2.5 - For Exercises 1 and 2, consider a group of regular...Ch. 2.5 - Given: ABDC, ADBC, AEFC, with angle measures as...Ch. 2.5 - In pentagon ABCDE with BDE, find the measure of...Ch. 2.5 - Find the total number of diagonals for a polygon...Ch. 2.5 - Find the total number of diagonals for a polygon...Ch. 2.5 - Find the sum of the measures of the interior...Ch. 2.5 - Find the sum of the measures of the interior...Ch. 2.5 - Find the measure of each interior angle of a...Ch. 2.5 - Find the measure of each interior angle of a...Ch. 2.5 - Find the sum of the measures of the exterior...Ch. 2.5 - Find the sum of the measures of the exterior...Ch. 2.5 - Find the measures of each exterior angle of a...Ch. 2.5 - Find the measures of each exterior angle of a...Ch. 2.5 - Find the number of sides for a polygon whose sum...Ch. 2.5 - Find the number of sides for a polygon whose sum...Ch. 2.5 - Find the number of sides for a regular polygon...Ch. 2.5 - Find the number of sides for a regular polygon...Ch. 2.5 - Find the number of sides for a regular polygon...Ch. 2.5 - Find the number of sides for a regular polygon...Ch. 2.5 - What is the measure of each interior angle of a...Ch. 2.5 - Lug bolts are equally spaced about the wheel to...Ch. 2.5 - In Exercises 23 to 28 , with P={allpolygons} as...Ch. 2.5 - In Exercises 23 to 28 , with P={allpolygons} as...Ch. 2.5 - In Exercises 23 to 28 , with P={allpolygons} as...Ch. 2.5 - In Exercises 23 to 28 , with P={allpolygons} as...Ch. 2.5 - In Exercises 23 to 28 , with P={allpolygons} as...Ch. 2.5 - In Exercises 23 to 28 , with P={allpolygons} as...Ch. 2.5 - Given: Quadrilateral RSTQ with exterior s at R and...Ch. 2.5 - Given: Regular hexagon ABCDEF with diagonal AC and...Ch. 2.5 - Given: Quadrilateral RSTV with diagonals RT and SV...Ch. 2.5 - Given: Quadrilateral ABCD with BAAD and BCDC...Ch. 2.5 - A father wishes to make a baseball home plate for...Ch. 2.5 - The adjacent interior and exterior angles of a...Ch. 2.5 - Find the measure of each a acute interior angle of...Ch. 2.5 - Find the measure of each a acute interior angle of...Ch. 2.5 - Consider any regular polygon; find and join in...Ch. 2.5 - Consider a regular hexagon RSTUVW. What does...Ch. 2.5 - The face of a clock has the shape of a regular...Ch. 2.5 - The top surface of a picnic table is in the shape...Ch. 2.5 - Consider a polygon of n sides deter-mined by the n...Ch. 2.5 - For the concave quadrilateral ABCD, explain why...Ch. 2.5 - If mA=20, mB=88 and mC=31, find the measure of the...Ch. 2.5 - Is it possible for a polygon to have the following...Ch. 2.5 - Is it possible for a regular polygon to have the...Ch. 2.5 - Draw a concave hexagon that has: a one interior...Ch. 2.5 - Draw a concave pentagon that has: a one interior...Ch. 2.5 - For concave pentagon ABCDE, find the measure of...Ch. 2.5 - For concave hexagon HJKLMN, mH=y and the measure...Ch. 2.5 - In concave hexagon HJKLMN, mH=72. Exterior angles...Ch. 2.6 - Which letters have symmetry with respect to a...Ch. 2.6 - Which letters have symmetry with respect to a...Ch. 2.6 - Which letters have symmetry with respect to a...Ch. 2.6 - Which letters have symmetry with respect to a...Ch. 2.6 - Which geometric figures have symmetry with respect...Ch. 2.6 - Which geometric figures have symmetry with respect...Ch. 2.6 - Which geometric figures have symmetry with respect...Ch. 2.6 - Which geometric figures have symmetry with respect...Ch. 2.6 - Which words have a vertical line of symmetry? DAD...Ch. 2.6 - Which words have a vertical line of symmetry? WOW...Ch. 2.6 - Complete each figure so that it has symmetry with...Ch. 2.6 - Complete each figure so that it has symmetry with...Ch. 2.6 - Complete each figure so that it reflects across...Ch. 2.6 - Complete each figure so that it reflects across...Ch. 2.6 - Suppose that ABC slides to right to the position...Ch. 2.6 - Suppose that square RSTV slides point for point to...Ch. 2.6 - Given that the vertical line is a line of...Ch. 2.6 - Given that the horizontal line is a line of...Ch. 2.6 - Given that the each letter has symmetry with...Ch. 2.6 - What word is produced by 180 rotation about the...Ch. 2.6 - What word is produced by 180 rotation about the...Ch. 2.6 - What word is produced by 360 rotation about the...Ch. 2.6 - In which direction clockwise or counterclockwise...Ch. 2.6 - In which direction clockwise or counterclockwise...Ch. 2.6 - Considering that the consecutive dials on the...Ch. 2.6 - Considering that the consecutive dials on the...Ch. 2.6 - Describe the types of symmetry displayed by each...Ch. 2.6 - Describe the types of symmetry displayed by each...Ch. 2.6 - Given a figure, which of the following pairs of...Ch. 2.6 - Given a figure, which of the following pairs of...Ch. 2.6 - A regular hexagon is rotated about a centrally...Ch. 2.6 - A regular octagon is rotated about a centrally...Ch. 2.6 - ABC is the image of ABC following the reflec- tion...Ch. 2.6 - XYZ is the image of XYZ following a 100...Ch. 2.6 - Hexagon ABCBAD is determined when the open figure...Ch. 2.6 - Rectangle BCAC is formed when the right ABC is...Ch. 2.CR - If m1=m2, which line segments are parallel?Ch. 2.CR - Given: m13=70 Find: m3Ch. 2.CR - Given: m9=2x+17m11=5x94 Find: xCh. 2.CR - Given: mB=75mDCE=50 Find: mD and mDEFCh. 2.CR - Given: mDCA=130mBAC=2x+ymBCE=150mDEC=2xy Find: x...Ch. 2.CR - Given: ACDFAEBFmAEF=3ymBFE=x+45mFBC=2x+15 Find: x...Ch. 2.CR - For Review Exercises 7 to 11 use the given...Ch. 2.CR - For Review Exercises 7 to 11, use the given...Ch. 2.CR - For Review Exercises 7 to 11, use the given...Ch. 2.CR - For Review Exercises 7 to 11, use the given...Ch. 2.CR - For Review Exercises 7 to 11, use the given...Ch. 2.CR - For Review Exercises 12 to 15 , find the values of...Ch. 2.CR - For Review Exercises 12 to 15 , find the values of...Ch. 2.CR - For Review Exercises 12 to 15, find the values of...Ch. 2.CR - For Review Exercises 12 to 15 , find the values of...Ch. 2.CR - Given: m1=x212 m4=x(x2) Find: x so that ABCDCh. 2.CR - Given: ABCDm2=x23x+4m1=17xx25mACE=111 Find: m3,...Ch. 2.CR - Given: DCAB ACmA=3x+ymD=5x+10mC=5y+20 Find: mBCh. 2.CR - For Review Exercises 19 to 24, decide whether the...Ch. 2.CR - For Review Exercises 19 to 24, decide whether the...Ch. 2.CR - For Review Exercises 19 to 24, decide whether the...Ch. 2.CR - For Review Exercises 19 to 24, decide whether the...Ch. 2.CR - For Review Exercises 19 to 24 , decide whether the...Ch. 2.CR - For Review Exercises 19 to 24, decide whether the...Ch. 2.CR - Complete the following table for regular polygons....Ch. 2.CR - For Review Exercises 26 to 29, sketch, if...Ch. 2.CR - For Review Exercises 26 to 29, sketch, if...Ch. 2.CR - For Review Exercises 26 to 29, sketch, if...Ch. 2.CR - For Review Exercises 26 to 29, sketch, if...Ch. 2.CR - For Review Exercises 30 and 31, write the...Ch. 2.CR - For Review Exercises 30 and 31, write the...Ch. 2.CR - Which statementthe converse, the inverse, or the...Ch. 2.CR - Given: ABCF23 Prove: 13Ch. 2.CR - Given: 1 is complementary to 2; 2 is complementary...Ch. 2.CR - Given: BEDACDDA Prove: 12Ch. 2.CR - Given: ACDCAB Prove: DACBCh. 2.CR - For Review Exercises 37 and 38 , give the first...Ch. 2.CR - For Review Exercises 37 and 38 , give the first...Ch. 2.CR - Given: mn Prove: 12Ch. 2.CR - Given: 13 Prove: mnCh. 2.CR - Construct the line through C parallel to AB.Ch. 2.CR - Construct an equilateral triangle ABC with side...Ch. 2.CR - Which block letters have a line symmetry at least...Ch. 2.CR - Which figures have a) line symmetry at least one...Ch. 2.CR - When ABC slides to its image DEF, how are ABC and...Ch. 2.CR - Complete the drawing so that the figure is...Ch. 2.CR - Through what approximate angle of rotation must a...Ch. 2.CT - Consider the figure shown at the right. a Name the...Ch. 2.CT - In the accompanying figure, m2=68, m8=112, and...Ch. 2.CT - To prove a theorem of the form "If P, then Q" by...Ch. 2.CT - Assuming that statements 1 and 2 are true, draw a...Ch. 2.CT - Let all of the lines named be coplanar. Make a...Ch. 2.CT - Through the point A, construct the line that is...Ch. 2.CT - For ABC, find mB if a mA=65 and mC=79. b mA=2x,...Ch. 2.CT - a What word describes a polygon with five sides? b...Ch. 2.CT - a Given that the polygon shown has six congruent...Ch. 2.CT - Consider the block letters A, D, N, O, and X....Ch. 2.CT - Which type of transformation slide, reflection, or...Ch. 2.CT - In the figure shown, suppose that ABDC and ADBC....Ch. 2.CT - If m1=x+28 and m2=2x26 find the value x for which...Ch. 2.CT - In the figure shown, suppose that ray CD bisects...Ch. 2.CT - In the figure shows, ACE is an exterior angle of...Ch. 2.CT - In Exercises 16 and 18 , complete the missing...Ch. 2.CT - In Exercise 16 and 18, complete the missing...Ch. 2.CT - In Exercises 16 and 18 , complete the missing...Ch. 2.CT - In XYZ, XYZ is trisected by YW and YV. With angle...

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