Step by step
The question
Question: prove that alternate angles are equal: ∠4 = ∠5.
We must show why ∠4 = ∠5 is always true.
Prove: = ∠4 = ∠5
Careful!
That is why the first row says the lines are parallel.
Careful: corresponding angles are equal
only when the lines are parallel
A proof is a table.
On the left: what we know.
On the right: why it is true.
1 Write what we know
The arrows show it: AB is parallel to CD.
AB ∥ CD
2 Use the angle facts
∠1 and ∠5 are in the same place at each crossing.
∠1 = ∠5
∠1 and ∠4 are opposite each other where two lines cross.
∠1 = ∠4
3 Reach the goal
∠4 and ∠5 are both equal to ∠1.
∠4 = ∠5
4 Check
Let's check: every row has a reason.
And the last row is what we had to prove: ∠4 = ∠5.
The proof is done!
Let's look back.
First: write what we know.
Then: use the angle facts.
Then: reach the goal.
Last: check.
Answer
Prove: = ∠4 = ∠5