Question

ABCD is a trapezoid with BC ∥ AD and ∠BAD ≅ ∠CDA. Which of the following statements are valid conclusions? Select True or False for each statement.

paralellogram9ma6new111

A. △AED ≅ △CDA
A True B False
B. △BAD ≅ △CDA
A True B False
C. AB ≅ BC
A True B False

Answer 1

From trapezoid ABCD, with BC║AD and ∠BAD≡∠CDA, then:

a] ΔAED is not similar to ΔCDA this is because ΔAED is an isosceles triangle because ∠BAD≡∠CDA, but ΔCDA is not isposceles, thus they cannot be similar.

b]ΔBAD≡ΔCDA, this is true because, the ratio of the corresponding sides are equal since they have the same angle properties in that they share similar angles.

c] AB is not similar to BC, this is because BC=CE≠AE