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
