Question

identifying triangle congruence practice
for each of the following:

1. state the reason the triangles are congruent: sss, sas, asa, aas, or hl. if they are not congruent, say

ot enough information\.

1. write the congruence statement. for example: $\triangle abc\cong \triangle def$

Explanation:

Step1: Analyze first triangle pair

All 3 corresponding sides are marked congruent.
Reason: SSS
Congruence: $\triangle ABC \cong \triangle DEF$

Step2: Analyze second triangle pair

2 sides and included angle congruent.
Reason: SAS
Congruence: $\triangle KML \cong \triangle NPQ$

Step3: Analyze third triangle pair

2 sides and included right angle congruent.
Reason: SAS (or HL, SAS applies here)
Congruence: $\triangle FRD \cong \triangle JTC$

Step4: Analyze fourth triangle pair

2 angles and non-included side congruent.
Reason: AAS
Congruence: $\triangle EFD \cong \triangle KLJ$

Step5: Analyze fifth triangle pair

2 angles and included side congruent.
Reason: ASA
Congruence: $\triangle GFH \cong \triangle VXU$

Step6: Analyze sixth triangle pair

Share side PR, 1 side + right angle congruent.
Reason: HL (right triangles)
Congruence: $\triangle PQR \cong \triangle PSR$

Step7: Analyze seventh triangle pair

Vertical angles + 2 sides congruent.
Reason: SAS
Congruence: $\triangle XYW \cong \triangle MYN$

Step8: Analyze eighth triangle pair

Share BD, 2 sides + right angle congruent.
Reason: HL (right triangles)
Congruence: $\triangle ABD \cong \triangle CBD$

Step9: Analyze ninth triangle pair

2 sides and included angle congruent.
Reason: SAS
Congruence: $\triangle JKM \cong \triangle JKL$

Step10: Analyze tenth triangle pair

Vertical angles + 2 sides congruent.
Reason: SAS
Congruence: $\triangle SRT \cong \triangle UTV$

Step11: Analyze eleventh triangle pair

2 angles and non-included side congruent.
Reason: AAS
Congruence: $\triangle KLJ \cong \triangle TRS$

Step12: Analyze twelfth triangle pair

All 3 corresponding sides congruent.
Reason: SSS
Congruence: $\triangle ZYW \cong \triangle XYW$

Step13: Analyze thirteenth triangle pair

2 sides and included angle congruent.
Reason: SAS
Congruence: $\triangle EFG \cong \triangle CBA$

Step14: Analyze fourteenth triangle pair

2 sides and non-included angle congruent.
Reason: Not enough information
Congruence: N/A

Step15: Analyze fifteenth triangle pair

2 sides and included right angle congruent.
Reason: HL (right triangles)
Congruence: $\triangle ABCD$: $\triangle ADC \cong \triangle BCD$

Step16: Analyze sixteenth triangle pair

2 angles and non-included side congruent.
Reason: AAS
Congruence: $\triangle SRT \cong \triangle ECD$

Step17: Analyze seventeenth triangle pair

2 sides and included right angle congruent.
Reason: HL (right triangles)
Congruence: $\triangle QRS \cong \triangle NML$

Step18: Analyze eighteenth triangle pair

Vertical angles + 2 sides congruent.
Reason: SAS
Congruence: $\triangle ABC \cong \triangle DEC$

Step19: Analyze nineteenth triangle pair

2 sides and included angle congruent.
Reason: SAS
Congruence: $\triangle XZY \cong \triangle CBD$

Step20: Analyze twentieth triangle pair

2 angles and included side congruent.
Reason: ASA
Congruence: $\triangle ABC \cong \triangle DEC$

Answer:

1. - Reason: SSS; Congruence: $\triangle ABC \cong \triangle DEF$
2. - Reason: SAS; Congruence: $\triangle KML \cong \triangle NPQ$
3. - Reason: SAS; Congruence: $\triangle FRD \cong \triangle JTC$
4. - Reason: AAS; Congruence: $\triangle EFD \cong \triangle KLJ$
5. - Reason: ASA; Congruence: $\triangle GFH \cong \triangle VXU$
6. - Reason: HL; Congruence: $\triangle PQR \cong \triangle PSR$
7. - Reason: SAS; Congruence: $\triangle XYW \cong \triangle MYN$
8. - Reason: HL; Congruence: $\triangle ABD \cong \triangle CBD$
9. - Reason: SSS; Congruence: $\triangle JKM \cong \triangle JKL$
10. - Reason: SAS; Congruence: $\triangle SRT \cong \triangle UTV$
11. - Reason: AAS; Congruence: $\triangle KLJ \cong \triangle TRS$
12. - Reason: SSS; Congruence: $\triangle ZYW \cong \triangle XYW$
13. - Reason: SAS; Congruence: $\triangle EFG \cong \triangle CBA$
14. - Reason: Not enough information; Congruence: N/A
15. - Reason: HL; Congruence: $\triangle ADC \cong \triangle BCD$
16. - Reason: AAS; Congruence: $\triangle SRT \cong \triangle ECD$
17. - Reason: HL; Congruence: $\triangle QRS \cong \triangle NML$
18. - Reason: SAS; Congruence: $\triangle ABC \cong \triangle DEC$
19. - Reason: SAS; Congruence: $\triangle XZY \cong \triangle CBD$
20. - Reason: ASA; Congruence: $\triangle ABC \cong \triangle DEC$