Prove triangles ABM and DCM are congruent: AM = DM, BM = CM

Step by step

The question

Question: prove that triangles ABM and DCM are congruent.

We know: AM = DM, BM = CM.

We must show why △ABM ≅ △DCM.

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.

AM = DM

Also given: BM = CM

2 Find more facts

The two lines cross at M.

∠AMB = ∠DMC

3 Reach the goal

Two sides and the angle between them: side, angle, side.

△ABM ≅ △DCM

4 Check

Let's check: every row has a reason.

And the last row is what we had to prove: △ABM ≅ △DCM.

The proof is done!

Let's look back.

First: write what we know.

Then: find more facts.

Then: reach the goal.

Last: check.