Question

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 Theorems

Triangles can be congruent by SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side), and HL (Hypotenuse - Leg for right - triangles).

Step2: Analyze Each Pair

1. For 1)

• There are two right - triangles. The hypotenuse (common side) and one leg (marked with equal signs) are equal. By HL (Hypotenuse - Leg) congruence criterion, the two triangles are congruent.

1. For 2)

• Two sides (marked with equal signs) and the included angle (common angle) are equal. By SAS (Side - Angle - Side) congruence criterion, the two triangles are congruent.

1. For 3)

• Two sides (marked with equal signs) and the non - included angle (not the angle between the two sides) are not sufficient for congruence. The triangles are not congruent.

1. For 4)

• Two sides (marked with equal signs) and the included angle (marked with equal signs) are equal. By SAS (Side - Angle - Side) congruence criterion, the two triangles are congruent.

1. For 5)

• Three sides (marked with equal signs) are equal. By SSS (Side - Side - Side) congruence criterion, the two triangles are congruent.

1. For 6)

• Three sides (marked with equal signs) are equal. By SSS (Side - Side - Side) congruence criterion, the two triangles are congruent.

1. For 7)

• The side - side - side combinations do not match. The triangles are not congruent.

1. For 8)

• Two angles (marked with equal signs) and a non - included side (common side) are equal. By AAS (Angle - Angle - Side) congruence criterion, the two triangles are congruent.

1. For 9)

• Two sides (marked with equal signs) and the included angle (not marked as equal) are not sufficient. The triangles are not congruent.

1. For 10)

• There are two right - triangles. The hypotenuse (marked with equal signs) and one leg (marked with equal signs) are equal. By HL (Hypotenuse - Leg) congruence criterion, the two triangles are congruent.

Answer:

1. Congruent (HL)
2. Congruent (SAS)
3. Not congruent
4. Congruent (SAS)
5. Congruent (SSS)
6. Congruent (SSS)
7. Not congruent
8. Congruent (AAS)
9. Not congruent
10. Congruent (HL)