Question

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

Explanation:

Step1: Analyze triangle 5

In the first pair of triangles (question 5), we only have two pairs of angles equal. AAA (Angle - Angle - Angle) is not a congruence criterion as it only shows similarity, not congruence.

Step2: Analyze triangle 7

In the second pair of triangles (question 7), we have two sides and the included angle equal. This is the SAS (Side - Angle - Side) congruence criterion.

Answer:

1. The two triangles are related by Angle - Angle - Angle (AAA), so the triangles CANNOT be proven congruent.
2. The two triangles are related by Side - Angle - Side (SAS), so the triangles can be proven congruent.