Lesson Practice A 4 - Jackson School District...Angles Postulate 10. n AEC > nBFD 10. ASA Congruence...
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Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Name ——————————————————————— Date ———————————— List all of the pairs of angles and sides that are congruent based on the given congruence statement and the figure. 1. n RST > n XZY 2. n ABC > n DEF R X S Z T Y A C B E D F Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? 3. ∠ C > ∠ F 4. } RT ù } LN 5. ∠ D ù ∠ H A B C D E F R S T N L M E G C F D H 6. ∠ STV > ∠ UTV 7. } EF ù } KJ 8. } XY ù } ZW T V S U E F J K D X Y W Z Is enough information given in the figure to show that the given statement is true? Explain. 9. ∠ N > ∠ Q 10. } RU > } TU 11. } FG > } HE M N P R R S U T G H F E Practice A For use with the lesson “Use Congruent Triangles” LESSON 4.7 Geometry Chapter Resource Book 4-89 LESSON 4.7
Transcript of Lesson Practice A 4 - Jackson School District...Angles Postulate 10. n AEC > nBFD 10. ASA Congruence...
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Name ——————————————————————— Date ————————————
List all of the pairs of angles and sides that are congruent based on the given congruence statement and the figure.
1. n RST > n XZY 2. n ABC > n DEF
R X
S Z
T Y
A
C B
E
D
F
Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use?
3. ∠ C > ∠ F 4. }
RT ù } LN 5. ∠ D ù ∠ H
A
B C
D
E F
R
S T
N
L M E G
C F
D
H
6. ∠ STV > ∠ UTV 7. }
EF ù } KJ 8. }
XY ù } ZW
T
V
S U
E F
J K
D
X Y
W Z
Is enough information given in the figure to show that the given statement is true? Explain.
9. ∠ N > ∠ Q 10. } RU > } TU 11. }
FG > } HE
M N
P
R
R S
U
T
G
H
F
E
Practice AFor use with the lesson “Use Congruent Triangles”
Less
on
4.7
GeometryChapter Resource Book 4-89
Lesson
4.7
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Name ——————————————————————— Date ————————————
Use the diagram to write a plan for a proof.
12. PROVE: ∠ J ù ∠ N 13. PROVE: } ST ù } UQ
L J
P N
K
R
S
T
U
R
Use the information given in the diagram to write a proof.
14. PROVE: ∠ ABD ù ∠ CBD 15. PROVE: } UV ù } WX
B
D A C
V
U W
X
16. Using angles You can position yourself halfway between two buildings of equal height by moving to a position where congruent angles are formed between the horizontal and your line of sight to the top of each building. Verify this by completing the three step proof below.
GIVEN: } AB ù } ED , ∠ ACB > ∠ ECD,
A
B
E
D
C
∠ A and ∠ E are right angles.
PROVE: } AC ù } EC
Statements Reasons
1. } AB ù } ED , ∠ ACB > ∠ ECD, 1. ? ∠ A and ∠ E are right angles.
2. n ABC > n EDC 2. ?
3. } AC ù } EC 3. ?
Practice A continuedFor use with the lesson “Use Congruent Triangles”
Les
so
n 4
.7
GeometryChapter Resource Book4-90
Lesson
4.7
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Statements Reasons
6. AC 5 CD 1 BC 6. Substitution property of equality
7. AC 5 BD 7. Substitution property of equality
8. } AC > }
BD 8. Definition of congruent segments
9. ∠ FDB > ∠ ECA 9. Corresponding Angles Postulate
10. n AEC > n BFD 10. ASA Congruence Postulate
6.
Statements Reasons
1. ∠ KNL > ∠ MNL, 1. Given ∠ KLN > ∠ MLN
2. } NL > }
NL 2. Reflexive property of congruence
3. n KNL > n MNL 3. ASA Congruence Postulate
4. } NK > }
NM 4. Corresponding parts of congruent triangles are congruent
5. m∠ JNK 1 m∠ KNL 5. Linear Pair 5 1808, Postulate m∠ JNM 1 m∠ MNL 5 1808
6. m∠ JNK 1 m∠ KNL 6. Transitive 5 m∠ JNM 1 property of m∠ MNL equality
7. m∠ KNL 5 m∠ MNL 7. Definition of congruent angles
8. m∠ JNK 1 m∠ KNL 8. Substitution 5 m∠ JNM 1 property of m∠ KNL equality
9. m∠ JNK 5 m∠ JNM 9. Subtraction property of equality
10. ∠ JNK > ∠ JNM 10. Definition of congruent angles
11. } JN > }
JN 11. Reflexive property of congruence
12. n JNK > n JNM 12. SAS Congruence Postulate
Lesson Use Congruent TrianglesTeaching Guide
1. SAS (all congruence assumed); corresponding parts of congruent triangles are congruent.
2.
SAS (one pair of sides congruent by reflexive property, one pair of sides assumed congruent, angles assumed congruent); corresponding parts of congruent triangles are congruent.
3. SAS (all congruence assumed); corresponding parts of congruent triangles are congruent.
4. SAS (both pairs sides assumed con-gruent, vertical angles congruent); corresponding parts of congruent triangles are congruent.
5.
SAS (one pair of sides congruent by reflexive property, one pair of sides assumed congruent, angles assumed congruent); corresponding parts of congruent triangles are congruent.
6. SAS (one pair of sides congruent by reflexive property, one pair of sides assumed congruent, angles assumed congruent); corresponding parts of congruent triangles are congruent.
Practice Level A
1. ∠ R > ∠ X, ∠ S > ∠ Z, ∠ T > ∠ Y, }
RS > } XZ , }
ST > } ZY , } RT > } XY 2. ∠ A > ∠ D, ∠ B > ∠ E, ∠ C > ∠ F,
} AB > } DE ,
} BC > } EF ,
}
AC > } DF 3. n ABC > n DEF; HL
4. n RST > n NML; AAS 5. n CDE > n FHG; ASA 6. n STV > n UTV; SSS 7. n DEF > n DKJ; SAS 8. XYZ > n ZWX; ASA
9. Yes; n MNP > n RQP by ASA, so ∠ N and ∠ Q are corresponding parts of > ns .
10. No; Only 2 pairs of sides can be assumed to be > in n RSU and n TSU, so there is not enough information to use congruent triangles.
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Lesson Prove Triangles Congruent by ASA and AAS, continued
GeometryChapter Resource Book A57
4.6 4.7
CS10_CC_G_MECR710761_C4AK.indd 57 4/28/11 6:14:11 PM
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11. Yes; n EFH > n GHF by AAS, so }
FG and } HE are corresponding parts of > ns . 12. Use SSS to prove n JKL > n NRP, then use the fact that ∠ J and ∠ N are corresponding parts of > ns .
13. Show because vertical angles, ∠ SRT > ∠ URQ. Use AAS to show n RST > n RUQ, then use the fact that
} ST
and }
UQ are corresponding parts of > ns
14. Statements Reasons
1. } AD > }
CD , } BD ⊥ }
AC 1. Given2. ∠ ADB and ∠ CDB 2. Thm 3.9
are right angles.3. ∠ ADB > ∠ CDB 3. All right angles
are >.4. } BD > } BD 4. Reflexive Prop. of
Congruence 5. n ADB > n CBD 5. SAS Congruence
Post.6. ∠ ABD > ∠ CBD 6. Corr. parts of > ns
are >. 15. Statements Reasons
1. } VW i } XU , ∠ VUW 1. Given and ∠ XWU are right angles.
2. } UW > } WU 2. Reflexive Prop. of Congruence
3. ∠ VUW > ∠ XWU 3. All right ? are >.4. ∠ VWU > ∠ XUW 4. Alt. Interior Angles
Thm.5. n UVW > n WXU 5. ASA Congruence
Post.6. } UV > } WX 6. Corr. parts of > ns
are >.16. Given; AAS Congruence Theorem; Corresponding parts of > ns are >.
Practice Level B
1. n ABC ù n CDA; SAS
2. n TSU ù n VSU; AAS
3. n ABD ù nC DB; SSS
4. n NKH ù n TMG; AAS
5. n ABD ù n CBE; ASA
6. n ABC ù n STA; AAS
7. Use the HL Congruence Theorem to prove that n DAB ù n BCD. Then use the fact that
corresponding parts of congruent triangles are congruent to prove that ∠ DAB ù ∠ BCD.
8. Because }
ST i } RQ , ∠ PRQ ù / RST by the Corresponding Angles Postulate. Use the ASA Congruence Postulate to prove that n PRQ ù n RST. Then use the fact that corresponding parts of congruent triangles are congruent to prove that
} ST ù
} RQ .
9. Use the Distance Formula to find the side lengths of the triangles. Use the SSS Congruence Postulate to show that n ABC ù n DEF. Then use the fact that corresponding parts of congruent triangles are congruent to prove that ∠ A ù ∠ D.
10. Use the Distance Formula to find the side lengths of the triangles. Use the SSS Congruence Postulate to show that n ABC ù n DEF. Then use the fact that corresponding parts of congruent triangles are congruent to prove that ∠ A ù ∠ D.
11. Given; Given; Definition of angle bisector; Reflexive Property of Congruence; SAS Congruence Postulate; Corresponding parts of congruent triangles are congruent.
12.
Statements Reasons
1. } MQ ù } NT 1. Given2. } MQ i } NT 2. Given3. ∠ NTM ù ∠ QMT 3. Alternate Interior
Angles Theorem4. } MT ù } MT 4. Reflexive Property of
Congruence5. n NTM ù n QMT 5. SAS Congruence
Postulate6. } MN ù
} TQ 6. Corresponding parts
of congruent triangles are congruent.
13.
Statements Reasons
1. } AB ù } BE 1. Given2. ∠ ADB ù ∠ ECB 2. Given3. ∠ ABD ù ∠ EBC 3. Vertical Angles
Theorem4. n ABD ù n EBC 4. AAS Congruence
Theorem5. } DB ù
} CB 5. Corresponding parts
of congruent triangles are congruent.
Practice Level C
1. n HGL > n JKM; AAS 2. n PQU > n VPS; AAS 3. n ABC > n DEF; ASA
Lesson Use Congruent Triangles, continued
GeometryChapter Resource BookA58
4.7
CS10_CC_G_MECR710761_C4AK.indd 58 4/28/11 6:14:12 PM
