Question

From the figure and statement provided, select the proper TO PROVE statement.

If two angles of a triangle are equal, the sides opposite those angles are equal
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Answer 1

Answer:

AB = BC Proved.

Step-by-step explanation:

See the diagram attached to this answer.

Given in a Δ ABC, ∠ A = ∠ C

Then we have to prove that AB = BC.

Let us draw a perpendicular from vertex B on the base AC and it intersects AC at D.

So, ∠ BDC = ∠ BDA = 90°

Now, between Δ ABD and Δ CBD,  

(i) BD is the common side.  

(ii)  ∠ BDC = ∠ BDA = 90° {Given}

and (iii) ∠ A = ∠ C {It is also given}

So, we can say  Δ ABD ≅ Δ CBD.

Therefore, AB = BC {Corresponding sides} (Proved)