Lesson Practice A 4 - Jackson School District...Angles Postulate 10. n AEC > nBFD 10. ASA Congruence Postulate 6. Statements Reasons 1. ∠ KNL > ∠ MNL, 1. Given ∠ KLN > ∠ MLN
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
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”
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.
an
sw
er
s
Lesson Prove Triangles Congruent by ASA and AAS, continued
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