Question

How to do given and proves ?

Answer 1

Hello from MrBillDoesMath!

Answer:   Relies on "vertical angle theorem" and sum of angles in a triangles is 180.

Discussion:

As angle(C) = angle(D)   (given) each triangle contains 1 identical angle. But angle(A), shared by both triangles, is a vertical angle so both triangles share this second identical angle. Now, a triangle has 180 degree, and both triangles already have 2 identical angles, the remaining third angles in each triangle ( i.e. angles, E, and B)  are identical.

For a clearer visualization of this, place a single tick spanning angles C and B,  and two ticks spanning angle A in each triangle.

Thank you,

MrB