Question

Are these triangles similar?

Answer 1

Answer:

B. Yes, by the AA Similarity Postulate

Step-by-step explanation:

This triangles are both similar based on the AA Similarity Postulate. We know that all angles are equal because...

m∠ABE = m∠CBD = 42° (because they are veridical/opposite angels)

m∠AEB = 180° - m∠ABE - m∠EAB = 180° - 42° - 53° = 85°

Then from here we know that

m∠BDC = 180° - 85° - m∠CBD

m∠BDC = 95° - 42°

m∠BDC = 53°

From here we see that they are similar because of the AA Similarity Postulate, since

m∠ABE = m∠CBD = 42°

m∠BDC = m∠EAB = 53°

m∠AEB = m∠BCD = 85°