Question

In the adjoining figure, AB = CD and angle ABC = angle BCD. Prove that (i) AC = BD
(ii) BE = CE. ​

Answer 1

Answer:

Step-by-step explanation:1. AC=BD

In triangle ABC and BCD

AB=CD(GIVEN)

ANGLE ABC=ANGLE BCD

BC=BC(COMMON)

therefore trinagles are congruent by sas

So,AC=BD

2.in triangle AEB AND CED

BC=BC (COMMON)

ANGLE AEB=ANGLE CED(VERTICALLY OPPOSITE ANGLES)

AC=BD(FROM1.)

SO, subtracting BE FROM both sides

Therefore AE=DE

SO triangles ar congruent by sas

So,BE=CE

Answer 2

Answer:

first prove the triangle ABC and DBC congruent