Question

estion #4: Explain if the triangles are similar using AA-. If they are similar, which angles are congruent and how do you know? (Explain your reasoning using evidence like a paragraph proof NOT a rigid motion proof!)

Answer 1

If the 2 triangles are similar, they will have the same measures for the 3 angles (3 pair of corresponding angles).

We know that the sum of the interior angles measures is equal to 180 degrees, so we can find the third angle for each of the triangles.

`\begin{gathered} m\angle B+68+54=180 \\ m\angle B=180-68-54 \\ m\angle B=58 \end{gathered}`

And for the other triangle, we have:

`\begin{gathered} m\angle E=180-68-63 \\ m\angle E=49 \end{gathered}`

As there is only one pair of congruent angles (F and A, that have the same measure), the triangles are not similar.

Answer: the triangles are not similar, as they only have one pair of congruent angles, when they should have 3 pairs of congruent angles.