Which confirms that ΔABC∼ΔA'B'C by the AA criterion?

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1 Answer
Jun 25, 2018

Choice D

Explanation:

First, we need to define what the AA #~=# AA theorem actually is.

This theorem is used for #color(dodgerblue)(similar)# triangles and states that if two triangles are similar, then their angles will be congruent.

So, we can set up an algebraic expression here.

We know that angle B is the exact same measure as angle B'.

Therefore: #color(dodgerblue)(6x-1=4x+21)#

Solve for x.

#color(dodgerblue)(x=11)#

Plug in x into the angle measure for angle B:
#color(dodgerblue)(6x-1)# #rarr# 6#color(dodgerblue)((11)#-1

You get that angle B is equal to 65 degrees. This matches choice D.

But wait, let's check that answer and make sure that angles C and C' are equal to 75 degrees.

So, we set up an equation that means that angle C must be equal to C': #color(dodgerblue)(8x-13=6x+9)#

Solve: #color(dodgerblue)(x=11)#

Plug in x=11 into the equation 8x-13, and you find that angle C=75 degrees. Assuming that this is the similar triangle, angle C' is also 75 degrees, so therefore, D is the correct answer.