Question

1. determine the relationship between the two triangles and whether or not they can be proven to be congruent.

the two triangles are related by
____________________, so the triangles
____________________.
word bank 1: (a) angle - angle - angle (aaa), (b) side - side - side (sss), (c) angle - side - angle (asa), (d) side - angle - side (sas), (e) hypotenuse - leg (hl), (f) side - side - angle (ssa), (g) angle - angle - side (aas)
word bank 2: (a) can be proven congruent, (b) cannot be proven congruent

1. determine the relationship between the two triangles and whether or not they can be proven to be congruent.

the two triangles are related by
____________________, so the triangles
____________________.
word bank 1: (a) angle - angle - angle (aaa), (b) side - angle - side (sas), (c) angle - angle - side (aas), (d) hypotenuse - leg (hl), (e) angle - side - angle (asa), (f) side - side - angle (ssa), (g) side - side - side (sss)
word bank 2: (a) can be proven congruent, (b) cannot be proven congruent

Explanation:

Step1: Analyze first pair of triangles

In the first pair, we have a right - angle, a marked side, and another marked side. This is the Hypotenuse - Leg (HL) criterion for right - triangles. Since both are right - triangles and the hypotenuse and one leg are congruent, they are congruent.

Step2: Analyze second pair of triangles

In the second pair, we have two sides and the included angle marked. This is the Side - Angle - Side (SAS) congruence criterion. So, the triangles are congruent.

Answer:

1. The two triangles are related by Hypotenuse - Leg (HL), so the triangles can be proven congruent.
2. The two triangles are related by Side - Angle - Side (SAS), so the triangles can be proven congruent.