Question

Choose the congruence theorem that you would use to prove the triangles congruent

Answer 1

The first one is correct since SSS states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are considered congruent.

For the second one HL would work appropriately since it states if the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are then considered congruent.

Answer 2

1. SAS
2. HL

Explanation:

In the first picture , we have two triangles where two sides and one include angle of first triangle is congruent to the corresponding two sides and one include angle.

Then by SAS-postulate of congruence, the both triangles are congruent.

In the second picture, we have two right triangle where hypotenuse and one leg of first triangle is congruent to the corresponding hypotenuse and one leg.

Then by HL theorem of congruence, the both triangles are congruent.