Question

sss, sas, and asa congruence
state if the two triangles are congruent. if they are, state how you know.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)

Explanation:

Step1: Recall congruence criteria

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

Step2: Analyze each pair of triangles

For each pair, check the marked sides and angles to see if they satisfy SSS, SAS, or ASA.

1. There are two sides and the included angle marked equal. So, the triangles are congruent by SAS.
2. There are two angles and the included side marked equal. So, the triangles are congruent by ASA.
3. All three sides are marked equal. So, the triangles are congruent by SSS.
4. There are two sides and the included angle marked equal. So, the triangles are congruent by SAS.
5. There are two sides and the included angle marked equal. So, the triangles are congruent by SAS.
6. There are two right - angles, the hypotenuse and one leg marked equal. This is the HL (Hypotenuse - Leg) criterion for right - triangles (but if we consider SSS, SAS, ASA only, we note that we can use SAS as we have two sides and the right - angle as the included angle). So, the triangles are congruent by SAS.
7. There are two sides and the included angle marked equal. So, the triangles are congruent by SAS.
8. All three sides are marked equal. So, the triangles are congruent by SSS.
9. There are two sides and the included angle marked equal. So, the triangles are congruent by SAS.
10. All three sides are marked equal. So, the triangles are congruent by SSS.

Answer:

1. Congruent by SAS
2. Congruent by ASA
3. Congruent by SSS
4. Congruent by SAS
5. Congruent by SAS
6. Congruent by SAS
7. Congruent by SAS
8. Congruent by SSS
9. Congruent by SAS
10. Congruent by SSS