Question

In the given figure, AE=BC and AB=CD.AE is perpendicular to AB and CD is perpendicular to BC

1) Show that triangle ABE is congruent to triangle CDB
2) Is angle ABE= angle CBD. Why or why not... Figure is in the given attachment

Answer 1

Answer:

1)  Side EA = Side BC (given)

   Side AB = Side CD (given)

    ∠A         = ∠C  (both are of the same measure)

Therefore, ΔABE ≅ ΔCDB by SAS congruency criteria.

2) Yes, since the two triangles are congruent, the two angles will also be equal.

Hope this helps...