Prove triangles ABC and DEF are congruent: angle A = angle D, angle…

Step by step

The question

Question: prove that triangles ABC and DEF are congruent.

We know: ∠A = ∠D, ∠B = ∠E, BC = EF.

We must show why △ABC ≅ △DEF.

Careful!

The letters go in the same order: the first letters match, the second letters match, and so on.

A proof is a table.

On the left: what we know.

On the right: why it is true.

1 Write what we know

First, what we are told.

∠A = ∠D

Also given: ∠B = ∠E

Also given: BC = EF

2 Reach the goal

Two angles and a side that is not between them: angle, angle, side.

△ABC ≅ △DEF

3 Check

Let's check: every row has a reason.

And the last row is what we had to prove: △ABC ≅ △DEF.

The proof is done!

Let's look back.

First: write what we know.

Then: reach the goal.

Last: check.