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?

Answer 1

Answer:

The triangles ABE and MNP are similar because the three corresponding angles are equal (AAA Criteria)

Step-by-step explanation:

we know that  

An isosceles triangle has two equal sides and two equal angles. The two equal angles are called the base angles and the third angle is called the vertex angle

The triangle ABE is an isosceles triangle with the vertex angle m∠ABE equal to $100\°$

so

m∠BAE=m∠AEB-------> base angles

m∠BAE+m∠AEB+m∠ABE= $180\°$ ------> sum of internal angles of triangle

Find m∠BAE

2m∠BAE=$180\°-100\°$

m∠BAE=$80\°/2=40\°$

The measure of the angles of triangle ABE are $40\°-100\°-40\°$

The triangle MNP is an isosceles triangle with the base angle m∠NMP and  m∠NPM equal to $40\°$

so

m∠MNP+m∠NMP+m∠NPM= $180\°$ ------> sum of internal angles of triangle

Find m∠MNP (vertex angle)

m∠MNP=$180\°-2*40\°$

m∠MNP=$100\°$

The measure of the angles of triangle MNP are $40\°-100\°-40\°$

therefore

The triangles ABE and MNP are similar because the three corresponding angles are equal (AAA Criteria)

Answer 2

Well since every triangle equals 180 and the definition of an isosceles is a triangle having two sides equal length which then means 2 equal angles to follow. This means that if one angle is 100 the next two angles would have to be 40 degrees. They are similar because they have the same degrees for the angles of both the triangles.