Name ________________________________________ Date __________________ Class__________________
LESSON
5-3
Practice B
Triangle Congruence: CPCTC
1. Heike Dreschler set the Woman’s World Junior Record for the
long jump in 1983. She jumped about 23.4 feet. The diagram
shows two triangles and a pond. Explain whether Heike
could have jumped the pond along path BA or along
path CA.
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Write a flowchart proof.
2. Given: ‘L > ‘J, KJ || LM
Prove: ‘LKM > ‘JMK
Write a two-column proof.
3. Given: FGHI is a rectangle.
Prove: The diagonals of a rectangle have equal lengths.
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Holt McDougal Analytic Geometry
6.
3. a. UJKM # ULKM or UJKM # UMKL
b. Proofs may vary.
7. 3; 5 ; 4 ; 3 ; 5 ; 4
9. CPCTC
4. Answers will vary.
Practice B
Problem Solving
1. Possible drawing:
2. Yes; the U is uniquely determined by AAS.
3. No; you need to know that ‘KJN and
‘LMN are rt. ‘s .
5. J
4. C
Reading Strategies
1. ASA
1. Possible answer: Because ‘DCE #
‘BCA by the Vertical ‘s Thm. the
triangles are congruent by ASA, and each
side in UABC has the same length as its
corresponding side in UEDC. Heike
could jump about 23 ft. The distance
along path BA is 20 ft because BA
corresponds with DE, so Heike could
have jumped this distance. The distance
along path CA is 25 ft because CA
corresponds with CE, so Heike could not
have jumped this distance.
2.
2. no conclusion
3. no conclusion
4. HL
5. AAS
6. ASA
3.
5-3 TRIANGLE CONGRUENCE: CPCTC
Statements
Practice A
1. Parts; Triangles
3. ‘A; ‘D
BC ; EF
8. SSS
2. AAS
AC ; DF
4. 5 m
5.
Statements
Reasons
1. PQ # RQ, ‘PQS #
‘RQS
1. Given
2. a. QS # QS
2. Reflexive Property
of #
3. b. UPQS # URQS
3. SAS
4. ‘P # ‘R
4. c. CPCTC
Reasons
1. FGHI is a rectangle.
1. Given
2. FI # GH, ‘FIH and ‘GHI
are right angles.
2. Def. of rectangle
3. ‘FIH # ‘GHI
3. Rt. ‘ # Thm.
4. IH # IH
4. Reflex. Prop. of #
5. UFIH # UGHI
5. SAS
6. FH # GI
6. CPCTC
7. FH
7. Def. of # segs.
GI
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Holt McDougal Analytic Geometry