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) hypotenuse - leg (hl), (b) side - side - side (sss), (c) angle - angle - side (aas), (d) side - side - angle (ssa), (e) side - angle - side (sas), (f) angle - angle - angle (aaa), (g) angle - side - angle (asa)
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) angle - angle - side (aas), (b) angle - side - angle (asa), (c) side - side - angle (ssa), (d) hypotenuse - leg (hl), (e) side - angle - side (sas), (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 2

In the first pair of triangles, we have a right - angle in each triangle, and one leg and the hypotenuse are marked as congruent. This is the Hypotenuse - Leg (HL) congruence criterion for right - triangles.

Step2: Determine congruence

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

Step3: Analyze triangle 4

In the second pair of triangles, we have two angles and a non - included side congruent. This is the Angle - Angle - Side (AAS) congruence criterion.

Step4: Determine congruence

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

Answer:

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