Question

Which theorem or postulate proves that △ABC and △DEF are similar?

Answer 1

Answer:

The triangles are similar by AA Similarity Postulate

Step-by-step explanation:

we know that

In the triangle ABC

m∠CAB=65°

m∠ABC=m∠CAB

so

m∠ABC=65°

Find the measure of angle ACB

Remember that

The sum of the internal angles in a triangle must be equal to 180 degrees

so

m∠ACB+m∠ABC+m∠CAB=180°

substitute the values

m∠ACB+65°+65°=180°

m∠ACB=180°-130°=50°

In the triangle DEF

m∠FDE=m∠CAB=65°

m∠DFE=50°

Find the measure of angle DEF

Remember that

The sum of the internal angles in a triangle must be equal to 180 degrees

so

m∠DEF+m∠FDE+m∠DFE=180°

substitute the values

m∠DEF+65°+50°=180°

m∠DEF=180°-115°=65°

therefore

m∠CAB=m∠FDE=65°

m∠ABC=m∠DEF=65°

m∠ACB=m∠DFE=50°

so

The three internal angles of the triangles are congruent

therefore

The triangles are similar by AA Similarity Postulate