Question

Given ΔABE is an isosceles triangle with ∠ABE = 100° and ΔMNP is an isosceles triangle with one base angle measuring 40°. Are the two triangles, ΔABE and ΔMNP similar? If so, by what criterion? A) yes, by AA criterion B) yes, by SAS criterion C) yes, by SSA criterion D) no, not possible to tell.

Answer 1

if both triangles are isosceles, that means they have two twin sides, and the twin sides make up twin angles on the other end.  Therefore, the triangles are similar by AA, check the picture below.

Answer 2

Yes, they are similar by the AA criterion

Explanation:

The AA criterion says if two triangles have two of their angles equal, the triangles are similar.

In this case you have: ΔABE is an isosceles triangle with ∠ABE = 100°, it means that the other angles only can be 40° and 40° (all the internal angles of a triangle must add 180°).

Remember that a isosceles triangle has two equal sides and the angles opposite the equal sides are also equal.

On the other hand you have ΔMNP is an isosceles triangle with one base angle measuring 40°, it mean that this triangle has its two base angles equal to 40°, and the other angle has to be 100°.

The conclusion is that this two isosceles triangles has the same angles.

The AA criterion is fullfilled.