Step by step
The question
Question: prove that triangles ABM and DCM are congruent, then that AB = DC.
We know: ∠A = ∠D, AM = DM.
We must show why △ABM ≅ △DCM and AB = DC.
Prove: = △ABM ≅ △DCM, AB = DC
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 C, M with M
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: AM = DM
2 Find more facts
The two lines cross at M.
∠AMB = ∠DMC
3 Reach the goal
Two angles and the side between them: angle, side, angle.
△ABM ≅ △DCM
AB and DC are in the same place in the two triangles.
AB = DC
4 Check
Let's check: every row has a reason.
And the last row is what we had to prove: AB = DC.
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: = △ABM ≅ △DCM, AB = DC