Step by step
The question
Question: prove that triangles ABD and CBD are congruent.
We know: AB = CB, ∠ABD = ∠CBD.
We must show why △ABD ≅ △CBD.
Prove: = △ABD ≅ △CBD
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 C, B with B, D with D
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 = CB
Also given: ∠ABD = ∠CBD
2 Find more facts
Look at the picture: BD is in both triangles.
BD = BD
3 Reach the goal
Two sides and the angle between them: side, angle, side.
△ABD ≅ △CBD
4 Check
Let's check: every row has a reason.
And the last row is what we had to prove: △ABD ≅ △CBD.
The proof is done!
Let's look back.
First: write what we know.
Then: find more facts.
Then: reach the goal.
Last: check.
Answer
Prove: = △ABD ≅ △CBD