Step by step
The question
Question: prove that triangles ABM and DCM are congruent.
M is the midpoint of AD and BC.
We must show why △ABM ≅ △DCM.
Prove: = △ABM ≅ △DCM
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 Find more facts
M is the midpoint: it cuts the line in half.
AM = DM
M is the midpoint: it cuts the line in half.
BM = CM
The two lines cross at M.
∠AMB = ∠DMC
2 Reach the goal
Two sides and the angle between them: side, angle, side.
△ABM ≅ △DCM
3 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: find more facts.
Then: reach the goal.
Last: check.
Answer
Prove: = △ABM ≅ △DCM