Question

Determine whether the triangles are similar. or not.

If similar, state how.

A. similar, AA
B. similar, sss
C. Similar, SAS
D. Not similar

Answer 1

A

Explanation:

We know that ∠
`ABE` ≅ ∠
`DBC` because they are vertical angles, so that's one pair of congruent angles. However, we can't compare ∠
`BAE` and ∠
`DCB` as they have different measures, so we'll have to find the measure of either ∠
`AEB` or ∠
`BDC`. Let's go with the former. Using the fact that the sum of the measures of the interior angles of a triangle is
`180`°, we know that
`m`∠
`AEB=180-(53+42)=180-95=85`°. Now, we know that ∠
`AEB` ≅ ∠
`DCB` because their measures are equal. That's another pair of congruent angles. Therefore, the angles are similar by
`AA`. Hope this helps!