Question

triangle congruence puzzle - 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. (video)
example:
1.
2.
3.
△abc≅△rwi by sas
△abc≅△ by
△abc≅△ by
4.
5.
6.
△ghj≅△ by
△abc≅△ by
△abc≅△ by
7.
8.
9.
△abc≅△ by
△def≅△ by
△jkl≅△ by
10.
11.
12.
△abc≅△ by
△abc≅△ by
△mno≅△ by
(when you are done with the puzzle, there are: 3 sas, 5 aas, 2 asa, and 2 sss instances.)
*delete an underscore as you fill in each letter in the puzzle to not mess up the numbers.

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 triangle 2

We have two angles and the included side of $\triangle ABC$ and $\triangle SEH$ are congruent. So $\triangle ABC\cong\triangle SEH$ by ASA.

Step3: Analyze triangle 3

We have two sides and the included angle of $\triangle ABC$ and $\triangle GNT$ are congruent. So $\triangle ABC\cong\triangle GNT$ by SAS.

Step4: Analyze triangle 4

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

Step5: Analyze triangle 5

We have two angles and a non - included side of $\triangle ABC$ and $\triangle SDT$ are congruent. So $\triangle ABC\cong\triangle SDT$ by AAS.

Step6: Analyze triangle 6

We have two angles and a non - included side of $\triangle ABC$ and $\triangle EHY$ are congruent. So $\triangle ABC\cong\triangle EHY$ by AAS.

Step7: Analyze triangle 7

We have all three sides of $\triangle ABC$ and $\triangle IHL$ are congruent. So $\triangle ABC\cong\triangle IHL$ by SSS.

Step8: Analyze triangle 8

We have two angles and a non - included side of $\triangle DEF$ and $\triangle SNA$ are congruent. So $\triangle DEF\cong\triangle SNA$ by AAS.

Step9: Analyze triangle 9

We have two angles and a non - included side of $\triangle JKL$ and $\triangle TAH$ are congruent. So $\triangle JKL\cong\triangle TAH$ by AAS.

Step10: Analyze triangle 10

We have two angles and a non - included side of $\triangle ABC$ and $\triangle GKP$ are congruent. So $\triangle ABC\cong\triangle GKP$ by AAS.

Step11: Analyze triangle 11

We have two angles and a non - included side of $\triangle ABC$ and $\triangle YED$ are congruent. So $\triangle ABC\cong\triangle YED$ by AAS.

Step12: Analyze triangle 12

We have two angles and a non - included side of $\triangle MNO$ and $\triangle KSA$ are congruent. So $\triangle MNO\cong\triangle KSA$ by AAS.

Answer:

1. $\triangle ABC\cong\triangle SEH$ by ASA
2. $\triangle ABC\cong\triangle GNT$ by SAS
3. $\triangle GHJ\cong\triangle EAR$ by AAS
4. $\triangle ABC\cong\triangle SDT$ by AAS
5. $\triangle ABC\cong\triangle EHY$ by AAS
6. $\triangle ABC\cong\triangle IHL$ by SSS
7. $\triangle DEF\cong\triangle SNA$ by AAS
8. $\triangle JKL\cong\triangle TAH$ by AAS
9. $\triangle ABC\cong\triangle GKP$ by AAS
10. $\triangle ABC\cong\triangle YED$ by AAS
11. $\triangle MNO\cong\triangle KSA$ by AAS