Step by step
The question
Question: prove that triangles ABC and DEF are congruent.
We know: ∠A = ∠D, AB = DE, ∠B = ∠E.
We must show why △ABC ≅ △DEF.
Prove: = △ABC ≅ △DEF
Careful!
The letters go in the same order: the first letters match, the second letters match, and so on.
Careful: the order of the letters matters
A with D, B with E, C with F
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: AB = DE
Also given: ∠B = ∠E
2 Reach the goal
Two angles and the side between them: angle, side, angle.
△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.
Answer
Prove: = △ABC ≅ △DEF