Question

given: angle 1 is congruent to angle 2, angle 3 is congruent to angle 4. AB=5cm, BC=5cm.prove: triangle AEB is congruent to triangle CEB(statements and reasons format and ignore other congruence markings)

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

∠ 1 ≅ ∠ 2

∠ 3 ≅ ∠ 4

AB = BC = 5 cm

Step 02:

We must apply the rules of congruent triangles to find the solution.

∠ 1 ≅ ∠ 2

∠ 3 ≅ ∠ 4

∠ A ≅ ∠ C

Δ AEB:

∠ 3 ===> angle

AB = 5 cm ===> side

∠ A ===> angle

Δ CEB:

∠ 4 ===> angle

BC = 5 cm ===> side

∠ C ===> angle

A-S-A rule (angle-side-angle):

Δ AEB ≅ Δ CEB, are congruent because all values are equal.

The answer is:

Applying the ASA rule we can conclude that both triangles are congruent.