G-CO.9: Day 15 Notes
Same-Side Interior Angles Postulate
Alternate Interior Angles Postulate
Corresponding Angles Theorem
Alternate Exterior Angles Postulate
Name______________________________________________
If two parallel lines are cut by a transversal, then the pairs of
same-side interior angles are supplementary.
If two parallel lines are cut by a transversal, then the pairs of
alternate interior angles have the same measure.
If two parallel lines are cut by a transversal, then the pairs of
corresponding angles have the same measure.
If two parallel lines are cut by a transversal, then the pairs of
alternate exterior angles have the same measure.
1. Explain how to find the m∠3 in the diagram if p ∥ q, and m∠6 = 61°
2. In the diagram, suppose p ∥ q and line t is perpendicular to line p. Can you conclude that line t is
perpendicular to line q?
3. In the diagram, suppose p ∥ q and m∠4 = 57°. Describe two different ways to determine m∠6.
4. In the diagram, suppose p ∥ q, explain why ∠1, ∠3, ∠5, 𝑎𝑛𝑑 ∠7 all have the same measure.
G-CO.9: Day 15 Notes
Name______________________________________________
Proofs about Parallel lines cut by transversals:
Proof: Alternate Interior Angles Theorem
Given: p ∥ q
Prove: m∠3 = m∠5
G-CO.9: Day 15 Notes
Name______________________________________________
Proof: Corresponding Angles Theorem
Given: p ∥ q
Prove: m∠1 = m∠5
Converse of Same-Side Interior Angles Postulate
Converse of Alternate Interior Angles Theorem
Converse of Corresponding Angles Theorem
Converse of Alternate Exterior Angles Theorem
If two lines are cut by a transversal so that a
pair of same-side interior angles are
supplementary, then the lines are parallel.
If two lines are cut by a transversal so that a
pair of alternate interior angles have the same
measure, then the lines are parallel.
If two lines are cut by a transversal so that a
pair of corresponding angles have the same
measure, then the lines are parallel.
If two lines are cut by a transversal so that a
pair of alternate exterior angles have the same
measure, then the lines are parallel.
G-CO.9: Day 15 Notes
Name______________________________________________
Prove the Converse of the Alternate Interior Angles Theorem.
Given: m∠3 = m∠5
Prove: p ∥ q