MATH SOLVE

4 months ago

Q:
# Which theorem or postulate proves that △ABC and △DEF are similar?-SAS Similarity Theorem-SSS Similarity Theorem-AA Similarity PostulateANSWER ASAP!Photo:

Accepted Solution

A:

Answer:The triangles are similar by AA Similarity PostulateStep-by-step explanation:we know thatIn the triangle ABCm∠CAB=65°m∠ABC=m∠CABsom∠ABC=65°Find the measure of angle ACBRemember thatThe sum of the internal angles in a triangle must be equal to 180 degreessom∠ACB+m∠ABC+m∠CAB=180°substitute the valuesm∠ACB+65°+65°=180°m∠ACB=180°-130°=50°In the triangle DEFm∠FDE=m∠CAB=65°m∠DFE=50°Find the measure of angle DEFRemember thatThe sum of the internal angles in a triangle must be equal to 180 degreessom∠DEF+m∠FDE+m∠DFE=180°substitute the valuesm∠DEF+65°+50°=180°m∠DEF=180°-115°=65°thereforem∠CAB=m∠FDE=65°m∠ABC=m∠DEF=65°m∠ACB=m∠DFE=50°soThe three internal angles of the triangles are congruentthereforeThe triangles are similar by AA Similarity Postulate