Question

triangle congruence practice
proving triangles congruent: asa, aas, sas, sss
for each problem give the correct naming order of the congruent triangles. write that name in order on the lines for the problem number (see box at bottom). also, indicate which postulate or theorem is being used.
(when you are done with the puzzle, there are: 3 sas, 5 aas, 2 asa, and 2 sss instances.)

Explanation:

Step1: Recall congruence postulates

ASA (Angle - Side - Angle): Two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. AAS (Angle - Angle - Side): Two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle. SAS (Side - Angle - Side): Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. SSS (Side - Side - Side): All three sides of one triangle are congruent to all three sides of another triangle.

Step2: Analyze each pair of triangles

Problem 2

We have two angles and the included side congruent. $\triangle ABC\cong\triangle ESH$ by ASA.

Problem 3

All three sides of $\triangle ABC$ are congruent to all three sides of $\triangle NGT$. So, $\triangle ABC\cong\triangle NGT$ by SSS.

Problem 4

We have two angles and a non - included side congruent. $\triangle GHJ\cong\triangle EAR$ by AAS.

Problem 5

We have two angles and a non - included side congruent. $\triangle ABC\cong\triangle DST$ by AAS.

Problem 6

We have two sides and the included angle congruent. $\triangle ABC\cong\triangle EHY$ by SAS.

Problem 7

All three sides of $\triangle ABC$ are congruent to all three sides of $\triangle LIH$. So, $\triangle ABC\cong\triangle LIH$ by SSS.

Problem 8

We have two angles and a non - included side congruent. $\triangle DEF\cong\triangle ANS$ by AAS.

Problem 9

We have two sides and the included angle congruent. $\triangle JKL\cong\triangle ATH$ by SAS.

Problem 10

We have two angles and a non - included side congruent. $\triangle ABC\cong\triangle KGP$ by AAS.

Problem 11

We have two angles and a non - included side congruent. $\triangle ABC\cong\triangle EDY$ by AAS.

Problem 12

We have two angles and a non - included side congruent. $\triangle MNO\cong\triangle ASK$ by AAS.

Answer:

1. $\triangle ABC\cong\triangle ESH$ by ASA
2. $\triangle ABC\cong\triangle NGT$ by SSS
3. $\triangle GHJ\cong\triangle EAR$ by AAS
4. $\triangle ABC\cong\triangle DST$ by AAS
5. $\triangle ABC\cong\triangle EHY$ by SAS
6. $\triangle ABC\cong\triangle LIH$ by SSS
7. $\triangle DEF\cong\triangle ANS$ by AAS
8. $\triangle JKL\cong\triangle ATH$ by SAS
9. $\triangle ABC\cong\triangle KGP$ by AAS
10. $\triangle ABC\cong\triangle EDY$ by AAS
11. $\triangle MNO\cong\triangle ASK$ by AAS