Step by step
The question
Question: prove that triangles ABC and DEF are congruent, then that ∠C = ∠F.
We know: AB = DE, BC = EF, AC = DF.
We must show why △ABC ≅ △DEF and ∠C = ∠F.
Prove: = △ABC ≅ △DEF, ∠C = ∠F
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.
AB = DE
Also given: BC = EF
Also given: AC = DF
2 Reach the goal
Three pairs of equal sides: side, side, side.
△ABC ≅ △DEF
∠C and ∠F are in the same place in the two triangles.
∠C = ∠F
3 Check
Let's check: every row has a reason.
And the last row is what we had to prove: ∠C = ∠F.
The proof is done!
Let's look back.
First: write what we know.
Then: reach the goal.
Last: check.
Answer
Prove: = △ABC ≅ △DEF, ∠C = ∠F