Question

directions: state if the two triangles are congruent. if they are, state how you know.

Explanation:

Step1: Identify congruence criteria for first pair

The first pair of triangles has three pairs of equal - length sides (side - side - side, SSS).

Step2: Identify congruence criteria for second pair

The second pair has a right - angle, a common side, and another pair of equal sides (hypotenuse - leg for right - triangles, HL, or side - angle - side, SAS considering the right - angle).

Step3: Identify congruence criteria for third pair

The third pair has three pairs of equal angles (angle - angle - angle, AAA), but AAA does not prove congruence, only similarity.

Step4: Identify congruence criteria for fourth pair

The fourth pair has two pairs of equal angles and a pair of equal sides (angle - side - angle, ASA).

Step5: Identify congruence criteria for fifth pair

The fifth pair has a right - angle, a pair of equal legs, and a pair of equal hypotenuses (hypotenuse - leg, HL).

Answer:

1. Congruent by SSS.
2. Congruent by HL or SAS.
3. Not congruent (AAA does not prove congruence).
4. Congruent by ASA.
5. Congruent by HL.