Question

in quadrilateral ABCD side BC <side AD figure 5.32 side bc parallel AD and if side BA congruent side CD then prove that angle ABC congruent angle DCB​

Answer 1

∠ABC ≅ ∠DCB

Step-by-step explanation:

First, we draw a segment DE parallel to BA, it meets BA at point E.

• It is given that BC is parallel to AD.

Also, we have AB ∥ ED (from the above construction)

• length of side AB = length of side DE  

Because, both are the distances between parallel lines BC & AD. So, They are equal.

Thus, opposite sides are parallel as well as equal in measures. Therefore, ABDE is a parallelogram.

• ∠ABE ≅ ∠DEC

Because, they are corresponding angles on the same side of transversal.

• length of BA = length of DE  

Because, they are opposite sides of a parallelogram ABDE.

Already, it is given that;

• Length of BA = length of CD

Then,

• length of DE = length of CD

Now, Δ CED has become isosceles triangle. Because, CE and CD are equal.

So, ∠CED and ∠DCE will be equal in measures.

• ∠CED ≅ ∠DCE

Beacuse, angle opposite to opposite sides are equal in measures.

Thus, we conclude that ∠ABC & ∠DCB are congruent.

                                ∠ABC ≅ ∠DCB

Answer 2

Answer:

Ok...

Step-by-step explanation:

I hope this Answers helps...