Question

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

Answer 1

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.