Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Chapter 1.CR, Problem 46CR
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Chapter 1 Solutions
Elementary Geometry For College Students, 7e
Ch. 1.1 - In Exercises 1 and 2, complete the statement....Ch. 1.1 - In Exercises 1 and 2, complete the statement....Ch. 1.1 - In Exercises 3 and 4, use the fact that...Ch. 1.1 - Prob. 4ECh. 1.1 - Prob. 5ECh. 1.1 - In Exercises 5 and 6, use the fact that...Ch. 1.1 - Eleanor finds the 15-mile road from A to C is...Ch. 1.1 - A cross-country runner jogs at a rate of 15 feet...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...
Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - Prob. 20ECh. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - Prob. 27ECh. 1.1 - In Exercises 9 to 28, use the drawings as needed...Ch. 1.1 - Prob. 29ECh. 1.1 - In Exercises 29 to 32, use only a compass and a...Ch. 1.1 - In Exercises 29 to 32, use only a compass and a...Ch. 1.1 - Prob. 32ECh. 1.1 - Can you use the construction for the midpoint of a...Ch. 1.1 - Generalize your findings in Exercise 33. 33. Can...Ch. 1.1 - Consider points A, B, C, and D, no three of which...Ch. 1.1 - Consider noncoplanar points A, B, C, and D. Using...Ch. 1.1 - Line l is parallel to plane P that is, it will not...Ch. 1.1 - AB and EF are said to be skew lines because they...Ch. 1.1 - Exercises 3840 In the box shown for Exercise 38,...Ch. 1.1 - Exercises 3940 In the box shown for Exercise 38,...Ch. 1.1 - Let AB=a and BC=b. Point M is the midpoint of BC....Ch. 1.2 - What type of angle has the given measure? a 47 b...Ch. 1.2 - What type of angle has the given measure? a 115 b...Ch. 1.2 - What relationship, if any, exists between two...Ch. 1.2 - What relationship, if any, exists between two...Ch. 1.2 - In Exercises 5 to 8, describe in one word the...Ch. 1.2 - In Exercises 5 to 8, describe in one word the...Ch. 1.2 - In Exercises 5 to 8, describe in one word the...Ch. 1.2 - In Exercises 5 to 8, describe in one word the...Ch. 1.2 - Use drawings as needed to answer each of the...Ch. 1.2 - Suppose that AB,AC,AD,AE, and AF are coplanar,...Ch. 1.2 - Exercises 10-13 Without using a protractor, name...Ch. 1.2 - Exercises 10-13 What, if anything, is wrong with...Ch. 1.2 - Exercises 10-13 FAC and CAD are adjacent and AF...Ch. 1.2 - For Exercises 14 and 15, let m1=x and m2=y. Using...Ch. 1.2 - For Exercises 14 and 15, let m1=x and m2=y. Using...Ch. 1.2 - Given: mRST=39 mTSV=23 Find: mRSV Exercises 1624Ch. 1.2 - Exercises 1624 Given: mRSV=59 mTSV=17 Find: mRSTCh. 1.2 - Exercises 1624 Given: mRST=2x+9 mTSV=3x2 mRSV=67...Ch. 1.2 - Exercises 1624 Given: mRST=2x10 mTSV=x+6...Ch. 1.2 - Exercises 1624 Given: mRST=5(x+1)3 mTSV=4(x2)+3...Ch. 1.2 - Exercises 1624 Given: mRST=x2 mTSV=x4 mRSV=45...Ch. 1.2 - Exercises 1624 Given: mRST=2x3 mTSV=x2 mRSV=49...Ch. 1.2 - Exercises 1624 Given: STbisectsRSV mRST=x+y...Ch. 1.2 - Exercises 1624 Given: STbisectsRSV mRST=2x+3y...Ch. 1.2 - Given: AB and AC in plane P as shown AD intersects...Ch. 1.2 - Two angles are complementary. One angle is 12...Ch. 1.2 - Two angles are supplementary. One angle is 24 more...Ch. 1.2 - For two complementary angles, find an expression...Ch. 1.2 - Suppose that the two angles are supplementary....Ch. 1.2 - On the protractor shown, NP bisects MNQ. Find x....Ch. 1.2 - Exercises 30,31 On the protractor shown for...Ch. 1.2 - Classify as true or false: a If points P and Q lie...Ch. 1.2 - Prob. 33ECh. 1.2 - Prob. 34ECh. 1.2 - In Exercises 33 to 40, use only a compass and a...Ch. 1.2 - Prob. 36ECh. 1.2 - Draw a triangle with three acute angles. Construct...Ch. 1.2 - Prob. 38ECh. 1.2 - Prob. 39ECh. 1.2 - Prob. 40ECh. 1.2 - Given: 1 and 2 as shown in, sketch the bisectors...Ch. 1.2 - Prob. 42ECh. 1.2 - Prob. 43ECh. 1.2 - If mTSV=38,mUSW=40, and mTSW=61, find mUSV....Ch. 1.2 - Exercises 44, 45 If mTSU=x+2z,mUSV=xz, and...Ch. 1.2 - Prob. 46ECh. 1.2 - On the hanging sign, the three angles...Ch. 1.2 - With 0x90, an acute angle has a measure x. Find...Ch. 1.3 - In Exercises 1 to 6, which property justifies the...Ch. 1.3 - In Exercises 1 to 6, which property justifies the...Ch. 1.3 - In Exercises 1 to 6, which property justifies the...Ch. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - In Exercises 1 to 6, which property justifies the...Ch. 1.3 - In Exercises 7 10, state the property or...Ch. 1.3 - In Exercises 7 10, state the property or...Ch. 1.3 - Prob. 9ECh. 1.3 - In Exercises 7 10, state the property or...Ch. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - In Exercises 11 to 22, use the Given information...Ch. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - In Exercises 11 to 22, use the Given information...Ch. 1.3 - Prob. 22ECh. 1.3 - In Exercises 23 to 24, fill in the missing reasons...Ch. 1.3 - In Exercises 23 to 24, fill in the missing reasons...Ch. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - In Exercises 27 to 30, fill in the missing reasons...Ch. 1.3 - In Exercises 27 to 30, fill in the missing reasons...Ch. 1.3 - In Exercises 27 to 30, fill in the missing reasons...Ch. 1.3 - In Exercises 31 and 32, fill in the missing...Ch. 1.3 - In Exercises 31 and 32, fill in the missing...Ch. 1.3 - Prob. 33ECh. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - The Division Property of Inequality requires that...Ch. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Write a proof for: If a=b and c=d, then ac=bd....Ch. 1.4 - In Exercise 1 and 2, supply reasons. Given: 13...Ch. 1.4 - In Exercise 1 and 2, supply reasons. Given: AB...Ch. 1.4 - In Exercise 3 and 4, supply statements. Given: 12...Ch. 1.4 - In Exercise 3 and 4, supply statements. Given:...Ch. 1.4 - In Exercise 5 to 9, use a compass and a...Ch. 1.4 - In Exercises 5 to 9, use a compass and a...Ch. 1.4 - In Exercise 5 to 9, use a compass and a...Ch. 1.4 - Prob. 8ECh. 1.4 - Prob. 9ECh. 1.4 - Prob. 10ECh. 1.4 - In Exercise 11 and 12, provide the missing...Ch. 1.4 - In Exercise 11 and 12, provide the missing...Ch. 1.4 - Does the relation is perpendicular to have a...Ch. 1.4 - Does the relation is greater than have a reflexive...Ch. 1.4 - Does the relation is complementary to for angles...Ch. 1.4 - Does the relation is less than for a numbers have...Ch. 1.4 - Does the relation is a brother of have a reflexive...Ch. 1.4 - Does the relation is a friend of have a reflexive...Ch. 1.4 - Prob. 19ECh. 1.4 - Sometimes symbols and abbreviations are used in...Ch. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prove the Extended Segment Addition Property by...Ch. 1.4 - The Segment-Addition Postulate can be generalized...Ch. 1.4 - Prove the Extended Angle Addition Property by...Ch. 1.4 - The Angle-Addition Postulate can be generalized as...Ch. 1.4 - Prob. 27ECh. 1.4 - In the proof below, provide the missing reasons....Ch. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.5 - In Exercises 1 to 6, state the hypothesis H and...Ch. 1.5 - In Exercises 1 to 6, state the hypothesis H and...Ch. 1.5 - In Exercises 1 to 6, state the hypothesis H and...Ch. 1.5 - In Exercises 1 to 6, state the hypothesis H and...Ch. 1.5 - Prob. 5ECh. 1.5 - In Exercises 1 to 6, state the hypothesis H and...Ch. 1.5 - Name, in order, the five parts of the formal proof...Ch. 1.5 - Which part hypothesis or conclusion of a theorem...Ch. 1.5 - Which part Given or Prove of the proof depends...Ch. 1.5 - Which of the following can be cited as a reason in...Ch. 1.5 - When can a theorem be cited as a reason reason in...Ch. 1.5 - Based upon the hypothesis of a theorem, do the...Ch. 1.5 - Prob. 13ECh. 1.5 - Prob. 14ECh. 1.5 - For each theorem stated in Exercises 13 to 18,...Ch. 1.5 - Prob. 16ECh. 1.5 - For each theorem stated in Exercises 13 to 18,...Ch. 1.5 - Prob. 18ECh. 1.5 - Prob. 19ECh. 1.5 - Prob. 20ECh. 1.5 - Prob. 21ECh. 1.5 - Prob. 22ECh. 1.5 - Prob. 23ECh. 1.5 - Prob. 24ECh. 1.5 - In Exercises 19 to 26, use the drawing in which AC...Ch. 1.5 - In Exercises 19 to 26, use the drawing in which AC...Ch. 1.5 - Prob. 27ECh. 1.5 - Prob. 28ECh. 1.5 - In Exercises 27 to 35, complete the formal proof...Ch. 1.5 - Prob. 30ECh. 1.5 - Prob. 31ECh. 1.5 - Prob. 32ECh. 1.5 - In Exercises 27 to 35, complete the formal proof...Ch. 1.5 - In Exercises 27 to 35, complete the formal proof...Ch. 1.5 - In Exercises 27 to 35, complete the formal proof...Ch. 1.CR - Name the four components of a mathematical system.Ch. 1.CR - Name three types of reasoning.Ch. 1.CR - Name the four characteristics of a good...Ch. 1.CR - In Review Exercises 4 to 6, name the type of...Ch. 1.CR - In Review Exercises 4 to 6, name the type of...Ch. 1.CR - In Review Exercises 4 to 6, name the type of...Ch. 1.CR - In Review Exercises 7 and 8, state the hypothesis...Ch. 1.CR - In Review Exercises 7 and 8, state the hypothesis...Ch. 1.CR - Prob. 9CRCh. 1.CR - Prob. 10CRCh. 1.CR - Prob. 11CRCh. 1.CR - A, B and C are three points on a line. AC=8, BC=4,...Ch. 1.CR - Prob. 13CRCh. 1.CR - Figure MNPQ is a rhombus. Draw diagonals MP and QN...Ch. 1.CR - In Review Exercises 15 to 17, sketch and label the...Ch. 1.CR - In Review Exercises 15 to 17, sketch and label the...Ch. 1.CR - In Review Exercises 15 to 17, sketch and label the...Ch. 1.CR - On the basis of appearance, what type of angle is...Ch. 1.CR - On the basis of appearance, what type of angle is...Ch. 1.CR - Given: BD bisects ABC mABD=2x+15 mDBC=3x+5 Find:...Ch. 1.CR - Given: mABD=2x+5 mDBC=3x4 mABC=86 Find: mDBCCh. 1.CR - Given: AM=3x1 MB=4x5 M is the midpoint of AB Find:...Ch. 1.CR - Given: AM=4x4 MB=5x+2 AB=25 Find: MBCh. 1.CR - Given: D is the midpoint of AC ACBC CD=2x+5...Ch. 1.CR - Given: m3=7x21 m4=3x+7 Find: mFMHCh. 1.CR - Given: mFMH=4x+1 m4=x+4 Find: m4Ch. 1.CR - In the figure, find: a KHFJ b MJMH c KMJJMH d MKMHCh. 1.CR - Given: EFG is a right angle. mHFG=2x6 mEFH=3mHFG...Ch. 1.CR - Two angles are supplementary. One angle is 40 more...Ch. 1.CR - aWrite an expression for the perimeter of the...Ch. 1.CR - The sum of the measures of all three angles of the...Ch. 1.CR - Susan wants to have a 4-ft board with some pegs on...Ch. 1.CR - State whether the sentences in Review Exercises 33...Ch. 1.CR - State whether the sentences in Review Exercises 33...Ch. 1.CR - State whether the sentences in Review Exercises 33...Ch. 1.CR - State whether the sentences in Review Exercises 33...Ch. 1.CR - State whether the sentences in Review Exercises 33...Ch. 1.CR - Fill in the missing statements or reasons. Given:...Ch. 1.CR - Write two-column proofs for Review Exercises 39 to...Ch. 1.CR - Write two-column proofs for Review Exercises 39 to...Ch. 1.CR - Prob. 41CRCh. 1.CR - Prob. 42CRCh. 1.CR - Prob. 43CRCh. 1.CR - Prob. 44CRCh. 1.CR - Prob. 45CRCh. 1.CR - Prob. 46CRCh. 1.CR - Given: VP Construct: VW such that VW=4VPCh. 1.CR - Prob. 48CRCh. 1.CR - Prob. 49CRCh. 1.CR - Prob. 50CRCh. 1.CR - Prob. 51CRCh. 1.CR - Prob. 52CRCh. 1.CT - Given ABC as shown, provide a second correct...Ch. 1.CT - Using the Segment-Addition Postulate, state a...Ch. 1.CT - Complete each postulate: a If two lines intersect,...Ch. 1.CT - Prob. 4CTCh. 1.CT - Prob. 5CTCh. 1.CT - Given that NP bisects MNQ, state a conclusion...Ch. 1.CT - Complete each theorem: a If two lines are...Ch. 1.CT - Given the line AC and ray BD, suppose that BE...Ch. 1.CT - Given that 2x3=7. What reason allows the...Ch. 1.CT - Given A-B-C-D, and M is the midpoint of AB. If...Ch. 1.CT - Prob. 11CTCh. 1.CT - In the figure, mEFG=68 and m3=33. Find m4.Ch. 1.CT - In the figure, m3=x and m4=2x3. If mEFG=69, find:...Ch. 1.CT - Prob. 14CTCh. 1.CT - Prob. 15CTCh. 1.CT - Prob. 16CTCh. 1.CT - Prob. 17CTCh. 1.CT - Construct the angle bisector of obtuse angle RST.Ch. 1.CT - Prob. 19CTCh. 1.CT - In exercises 20 to 22, complete the missing...Ch. 1.CT - Prob. 21CTCh. 1.CT - In exercises 20 to 22, complete the missing...Ch. 1.CT - Prob. 23CT
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- In the proof below, provide the missing reasons. Given: 1 and 2 are complementary 1 is acute Prove: 2 is acute PROOF Statements Reasons 1. 1 and 2 are complementary 1. ? 1 2. m1+m2=90 2. ? 3. 1 is acute 3. ? 3 4. Where m1=x, 0x90 4. ? 2 5. x+m2=90 5. ? 5 6. m2=90x 6. ? 4 7. x090x 7. ? 7 8. 90x90180x 8. ? 7, 8 9. 090x90 9. ? 6, 9 10. 0m/290 10. ? 10 11. 2 is acute 11. ?arrow_forwardIn the proof below, provide the missing reasons. Given: 1 and 2 are complementary 1 is acute Prove: 2 is also acute PROOF Statements Reasons 1. 1 and 2 are complementary 1. ? 1 2. m1+m2=90 2. ? 3. 1 is acute 3. ? 3 4. Where m1=x, 0x90 4. ? 2 5. x+m2=90 5. ? 5 6. m2=90x 6. ? 4 7. x090x 7. ? 7 8. 90x90180x 8. ? 7, 8 9. 090x90 9. ? 6, 9 10. 0m/290 10. ? 10 11. 2 is acute 11. ?arrow_forwardThe Segment-Addition Postulate can be generalized as follows: The length of a line segment equals the sum of the length of its parts. State a general conclusion regarding AE based on the following figure.arrow_forward
- Prove that if (a,b,c) is a Pythagorean triple and n is a natural number, the (na,nb,nc) is also a Pythagorean triple.arrow_forwardIn a right triangle, the sides that form the right angle are the legs; the longest side opposite the right angle is the hypotenuse. Some textbooks say that when two right triangles have congruent pairs of legs, the right triangles are congruent by the reason LL. In our work, LL is just a special case of one of the postulates in this section. Which postulate is that?arrow_forwardWhich of the following statements would you prove by the indirect method? a If ACAB in ABC, then mBmC. b If AC=AB in ABC, then mB=mC. c If RSTV is not a square, then RSST. d An angle has exactly one bisector.arrow_forward
- The diagram shown in Figure 1 was used by the Hindu mathematician Bhaskara to prove the theorem in the 12th century. His proof consisted only of the diagram and the word Behold! Use this figure to derive the Pythagorean Theorem. The right triangle with sides a, b, and c has been repeated three times. The area of the large square is equal to the sum of the areas of the four triangles and the area of the small square in the center. The key to this derivation is in finding the length of a side of the small square. Once you have the equation, simplify the right side to obtain the theorem. Figure 1arrow_forwardIn Exercise 11 and 12, provide the missing statements and reasons. Given: 12;34 s 2 and 3 are complementary Prove: s 1 and 4 are complementary PROOF Statements Reasons 1. 13 and 34 1. ? 2. ? and ? 2. If two s are , then their measures are equal. 3. s 2 and 3 are complementary 3. ? 4. ? 4. The sum of the measures of complementary s is 90 5. m1+m4=90 5. ? 6. ? 6. If the sum of the measures of two angles is 90, then the angles are complementaryarrow_forwardA carpenter lays out boards of lengths 8 ft, 8 ft, 4 ft, and 4 ft by placing them end to end. a If these are joined at the ends to form a quadrilateral that has the 8-ft pieces connected in over, what type of quadrilateral is formed? b If these are joined at the ends to form a quadrilateral that has the 4-ft and 8-ft pieces alternating, what type of quadrilateral is formed?arrow_forward
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