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
___ word bank 1
___ word bank 2
word bank 1: (a) angle - angle - angle (aaa), (b) hypotenuse - leg (hl), (c) side - side - side (sss), (d) side - angle - side (sas), (e) side - side - angle (ssa), (f) angle - side - angle (asa), (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
___ word bank 1
___ word bank 2
word bank 1: (a) angle - side - angle (asa), (b) angle - angle - side (aas), (c) side - side - side (sss), (d) side - side - angle (ssa), (e) hypotenuse - leg (hl), (f) side - angle - side (sas), (g) angle - angle - angle (aaa)
word bank 2: (a) can be proven congruent, (b) cannot be proven congruent

Explanation:

Step1: Analyze first pair of triangles

In the first pair, two sides and the included - angle of one triangle are equal to two sides and the included - angle of the other triangle. This is the Side - Angle - Side (SAS) congruence criterion.

Step2: Determine congruence for first pair

Since the SAS criterion is met, the triangles can be proven congruent.

Step3: Analyze second pair of triangles

In the second pair, two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of the other triangle. This is the Angle - Angle - Side (AAS) congruence criterion.

Step4: Determine congruence for second pair

Since the AAS criterion is met, the triangles can be proven congruent.

Answer:

1. The two triangles are related by (d) Side - Angle - Side (SAS), so the triangles (a) can be proven congruent.
2. The two triangles are related by (b) Angle - Angle - Side (AAS), so the triangles (a) can be proven congruent.