Question

See the picture :D. Please help fast.

Answer 1

In ΔABD and ΔAEC

BE=DC (given) …(i)

Subtracting DE from both side of (i), we get

BE–DE=DC–DE

BD=EC

AB=AC (given)

∠B=∠C (angle opposite to equal sides are equal)

Similarly, ΔABD≅ΔAEC

AD=AE (by c.p.c.t)

Hence proved

Answer 2

• See below

Explanation:

Consider triangles ABE and ACD:

• ∠BAC ≅ ∠CAB, common angle, congruent to itself
• ∠ABE ≅ ∠ACD, same arc DE intercepted
• AB = AC, given

According to above congruence statements, we can conclude:

• ΔABE ≅ ΔACD as per ASA postulate, since two angles and the included side are congruent

Since the triangles are congruent, we have:

• BE = CD as corresponding sides of congruent triangles