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6th Edition

Daniel C. Alexander + 1 other

Publisher: Cengage Learning

ISBN: 9781285195698

Chapter 2.4, Problem 42E

Textbook Problem

A polygon with four sides is called *quadrilateral*. Consider the figure and the dashed auxiliary line. What is the sum of the measures of the four interior angles of this (or any other) quadrilateral?

Elementary Geometry for College Students

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Ch. 2.1 - For Exercises 1 to 4, lm with transversal v. If...Ch. 2.1 - For Exercises 1 to 4, lm with transversal v. If...Ch. 2.1 - For Exercises 1 to 4, lm with transversal v. If...Ch. 2.1 - For Exercises 1 to 4, lm with transversal v. If...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. 2.2 - 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 - In Exercises 12 to 14, write the first statement...Ch. 2.2 - In Exercises 12 to 14, write the first statement...Ch. 2.2 - In Exercises 12 to 14, write the first statement...Ch. 2.2 - For Exercises 15 to 18, the given statement is...Ch. 2.2 - For Exercises 15 to 18, the given statement is...Ch. 2.2 - For Exercises 15 to 18, the given statement is...Ch. 2.2 - For Exercises 15 to 18, the given statement is...Ch. 2.2 - In Exercise 19 and 20, state a conclusion for the...Ch. 2.2 - In Exercise 19 and 20, 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 23 to 34, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 34, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 34, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 35, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 34, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 32, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 32, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 32, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 32, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 32, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 34, give the indirect proof for...Ch. 2.2 - In Exercises 23 to 34, 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. 2.4 - 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 rt 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 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 21 to 26, with P={allpolygons} as the...Ch. 2.5 - In Exercises 21 to 26, with P={allpolygons} as the...Ch. 2.5 - In Exercises 21 to 26, with P={allpolygons} as the...Ch. 2.5 - In Exercises 21 to 26, with P={allpolygons} as the...Ch. 2.5 - In Exercises 21 to 26, with P={allpolygons} as the...Ch. 2.5 - In Exercises 21 to 26, with P={allpolygons} as the...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. 2.6 - 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 lines 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...Ch. 2.CT - a What word describes a polygon with five sides?...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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