Step by step
The question
Question: prove that triangles ABD and CBD are congruent, then that AB = CB.
We know: ∠A = ∠C, ∠ABD = ∠CBD.
We must show why △ABD ≅ △CBD and AB = CB.
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 = ∠C
Also given: ∠ABD = ∠CBD
2 Find more facts
Look at the picture: BD is in both triangles.
BD = BD
3 Reach the goal
Two angles and a side that is not between them: angle, angle, side.
△ABD ≅ △CBD
AB and CB are in the same place in the two triangles.
AB = CB
4 Check
Let's check: every row has a reason.
And the last row is what we had to prove: AB = CB.
The proof is done!
Let's look back.
First: write what we know.
Then: find more facts.
Then: reach the goal.
Last: check.