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
so
m∠BAE=m∠AEB-------> base angles
m∠BAE+m∠AEB+m∠ABE= ------> sum of internal angles of triangle
Find m∠BAE
2m∠BAE=
m∠BAE=
The measure of the angles of triangle ABE are
The triangle MNP is an isosceles triangle with the base angle m∠NMP and m∠NPM equal to
so
m∠MNP+m∠NMP+m∠NPM= ------> sum of internal angles of triangle
Find m∠MNP (vertex angle)
m∠MNP=
m∠MNP=
The measure of the angles of triangle MNP are
therefore
The triangles ABE and MNP are similar because the three corresponding angles are equal (AAA Criteria)