Question

practice triangle congruence by sss, sas, asa, aas
determine if the two triangles are congruent. if they are, state how you know (sss, sas, asa, aas).
1)
2)
3)
4)
5)

Explanation:

Step1: Analyze Problem 1

The two triangles share a common side. The other two sides of each triangle are marked as equal (two pairs of congruent sides) and the included sides (the base) are also marked equal. So by SSS (Side - Side - Side) congruence criterion, the triangles are congruent.

Step2: Analyze Problem 2

There is a pair of vertical angles (which are equal) and two pairs of congruent sides (marked with ticks). So by SAS (Side - Angle - Side) congruence criterion (the angle is between the two sides), the triangles are congruent.

Step3: Analyze Problem 3

There is a right angle in each triangle, a common side (the altitude), and a pair of congruent angles (the base angles). So by AAS (Angle - Angle - Side) or ASA (Angle - Side - Angle) congruence criterion (since we have a right angle, a common side, and a non - included angle or included angle), the triangles are congruent (AAS or ASA, AAS is more appropriate here as we have two angles and a non - included side).

Step4: Analyze Problem 4

There is a pair of congruent sides (marked), a common side, and the included angle (marked as equal). So by SAS (Side - Angle - Side) congruence criterion, the triangles are congruent.

Step5: Analyze Problem 5

There is a common side, a pair of congruent angles (marked), and a pair of congruent sides (the other sides). So by SAS (Side - Angle - Side) congruence criterion, the triangles are congruent.

Answer:

1. Congruent by SSS.
2. Congruent by SAS.
3. Congruent by AAS.
4. Congruent by SAS.
5. Congruent by SAS.