Question

Given: angle 1 is congruent to angle 2, angle 3 is congruent to angle four. AB= 5cm, BC= 5cm.prove: triangle AEB is congruent to triangle CEB(statements and reasons format, ignore congruence marking)

Answer 1

The two triangles are similar by side-angle-side

Here, we want to prove that triangle AEB is congruent to CEB

For both to be congruent, there must be some congruence rule that links both

Let us start with triangles FAB and BCD

Since two of the angles are equal, it is sure that the third angles are equal

Thus;

angle FAB = angle BCD

So, firstly, we have one of the angles of both triangles equal

Secondly, we already have it that AB = BC = 5

This means that we also have a side of each equal

Lastly, as we can see from the diagram, the side EB is common to both triangles, and this makes up for the third fact that the triangles are equal

So from all these, we have two equal sides and an equal angle

So, the congruence statement is SAS (side-angle-side)