Question

Given ABE is an isosceles triangle with ZABE - 100° and AMNP is an isosceles triangle with one base angle measuring 40°. Are

the two triangles, ABE and MNP similar? If so, by what criterion?
A)
yes, by AA criterion
B)
yes, by SAS criterion
yes, by SSA criterion
no, not possible to tell

Answer 1

Two triangle ABE and MNP are similar by AA criterion

Explanation:

Given that ABE is an isosceles Δ with ABE= 100°

this means that some of the other two angles must be =180°-100°=80°

Since the triangle is an isosceles Δ meaning two sides measure must be equal, it means the other two sides measure 40° each.

∠BAC=∠ACB=40°

In MNP one of the base angles is 40° and the triangle is isosceles. For an isosceles triangle base angles are always equal hence other base angle is also 40° meaning

the angle measures come out to be 40°,40° and 100°

Since all the angle measures are same the two triangles are similar in aspect by AA criterion where AA refers to "angle-angle"