Step by step
The question
Question: prove that co-interior angles add up to 180°: ∠4 + ∠6 = 180°.
We must show why ∠4 + ∠6 = 180° is always true.
Prove: = ∠4 + ∠6 = 180°
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
∠2 and ∠6 are in the same place at each crossing.
∠2 = ∠6
∠2 and ∠4 sit side by side on a straight line.
∠2 + ∠4 = 180°
3 Reach the goal
∠2 is the same size as ∠6.
∠6 + ∠4 = 180°
4 Check
Let's check: every row has a reason.
And the last row is what we had to prove: ∠6 + ∠4 = 180°.
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 + ∠6 = 180°