Elementary Geometry for College Students
6th Edition
ISBN: 9781285195698
Author: Daniel C. Alexander, Geralyn M. Koeberlein
Publisher: Cengage Learning
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Textbook Question
Chapter 2.2, Problem 4E
Note: Exercises preceded by an asterisk are of a more challenging nature.
In Exercises 1 to 4, write the converse, the inverse, and the contrapositive of each statement. When possible, classify the statement as true or false.
In a plane, if two lines are not perpendicular to the same line, then these lines are not parallel.
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Students have asked these similar questions
Translate the mathematical statement into symbolic form.
If two sides of a triangle are equal in length (p), the angles opposite those sides are congruent (q).
Statement
If two lines intersect,
creating vertical angles,
then the vertical angles are
congruent.
Given:
Conclusion:
If two lines intersect,
creating vertical angles,
then the vertical angles are
congruent.
Given: Two lines intersect,
creating vertical angles.
Conclusion: The vertical
angles are congruent.
Conclusion:
Conclusion:
Given: Two lines intersect,
creating vertical angles.
For the following problems, fill out as much information as possible.
Statement
Notation
1. If AABC is an isosceles
triangle, then angle A is
congruent to angle C.
Given:
Given:
Notation
Conclusion: ZNMA =
ZRMT
Conclusion:
Given:
2. If AB is an angle bisector Given:
of ZMAT, then the angles
created by the bisector are
congruent.
Given:
Conclusion:
3. If AB is a perpendicular
bisector of MN at point B,
then MB is congruent to BN.
Conclusion:
Given:
N
Conclusion:
N
Picture
A
M
Picture
B
M
R
C
Directions: For the given statement, determine the inverse, converse and
contrapositive.
If a triangle is isosceles, then it has two congruent angles.
1.
Converse:
Inverse:
Contrapositive:
2.
If you are a reader, then you are a learner.
Converse:
Inverse:
Contrapositive:
3.
If Nemo is a fish, then he swims.
Converse:
Inverse:
Contrapositive:
4.
If you don't work, then you don't have a salary.
Converse:
Inverse:
Contrapositive:
If you play the piano, then you are a musician.
5.
Converse:
Inverse:
Contrapositive:
Chapter 2 Solutions
Elementary Geometry for College Students
Ch. 2.1 - Prob. 1ECh. 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 - Prob. 4ECh. 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 - Prob. 26ECh. 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 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Given: Triangle MNQ with obtuse MNQ Construct:...Ch. 2.1 - Prob. 35ECh. 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 - Prob. 3ECh. 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 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Which of the following statements would you prove...Ch. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - A periscope uses an indirect method of...Ch. 2.2 - Some stores use an indirect method of observation....Ch. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - In Exercises 23 to 34, give the indirect proof for...Ch. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 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 - Prob. 3ECh. 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 - Prob. 17ECh. 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 - Prob. 31ECh. 2.3 - In Exercises 31 to 33, give a formal proof for...Ch. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 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 - Prob. 19ECh. 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 - Prob. 27ECh. 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 - Prob. 31ECh. 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 - Prob. 34ECh. 2.4 - Along a straight shoreline, two houses are located...Ch. 2.4 - An airplane has leveled off is flying horizontally...Ch. 2.4 - Prob. 37ECh. 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 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Explain why the following statement is true. The...Ch. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 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 - Prob. 50ECh. 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 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 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 - Prob. 39ECh. 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 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Which letters have symmetry with respect to a...Ch. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Prob. 12ECh. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Suppose that square RSTV slides point for point to...Ch. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - In which direction clockwise or counterclockwise...Ch. 2.6 - In which direction clockwise or counterclockwise...Ch. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - A regular hexagon is rotated about a centrally...Ch. 2.6 - A regular octagon is rotated about a centrally...Ch. 2.6 - Prob. 33ECh. 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 - Prob. 36ECh. 2.CR - Prob. 1CRCh. 2.CR - Prob. 2CRCh. 2.CR - Prob. 3CRCh. 2.CR - Prob. 4CRCh. 2.CR - Given: mDCA=130mBAC=2x+ymBCE=150mDEC=2xy Find: x...Ch. 2.CR - Prob. 6CRCh. 2.CR - Prob. 7CRCh. 2.CR - Prob. 8CRCh. 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 - Prob. 12CRCh. 2.CR - Prob. 13CRCh. 2.CR - Prob. 14CRCh. 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 - Prob. 17CRCh. 2.CR - Prob. 18CRCh. 2.CR - Prob. 19CRCh. 2.CR - For Review Exercises 19 to 24, decide whether the...Ch. 2.CR - Prob. 21CRCh. 2.CR - Prob. 22CRCh. 2.CR - Prob. 23CRCh. 2.CR - Prob. 24CRCh. 2.CR - Complete the following table for regular polygons....Ch. 2.CR - Prob. 26CRCh. 2.CR - For Review Exercises 26 to 29, sketch, if...Ch. 2.CR - For Review Exercises 26 to 29, sketch, if...Ch. 2.CR - Prob. 29CRCh. 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 - Prob. 35CRCh. 2.CR - Given: ACDCAB Prove: DACBCh. 2.CR - Prob. 37CRCh. 2.CR - Prob. 38CRCh. 2.CR - Prob. 39CRCh. 2.CR - Prob. 40CRCh. 2.CR - Prob. 41CRCh. 2.CR - Construct an equilateral triangle ABC with side...Ch. 2.CR - Prob. 43CRCh. 2.CR - Prob. 44CRCh. 2.CR - Prob. 45CRCh. 2.CR - Complete the drawing so that the figure is...Ch. 2.CR - Prob. 47CRCh. 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 - Prob. 6CTCh. 2.CT - Prob. 7CTCh. 2.CT - Prob. 8CTCh. 2.CT - Prob. 9CTCh. 2.CT - Prob. 10CTCh. 2.CT - Prob. 11CTCh. 2.CT - Prob. 12CTCh. 2.CT - Prob. 13CTCh. 2.CT - Prob. 14CTCh. 2.CT - Prob. 15CTCh. 2.CT - In Exercises 16 and 18 , complete the missing...Ch. 2.CT - Prob. 17CTCh. 2.CT - Prob. 18CTCh. 2.CT - Prob. 19CT
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