Cogito
Geometry · Chapter 1 · Lesson 2
Angle Pairs and Parallel Lines
A transversal makes eight angles and only two sizes.
11 problems · about 23 minutes · G-CO.C.9
What this lesson teaches
The student uses angle relationships formed by a transversal to find unknown angles.
- Vertical angles are equal wherever two lines cross.
- With parallel lines, corresponding and alternate angles are equal and co-interior ones add to 180°.
- Eight angles, but only two sizes: find one and the rest follow.
Warm Up
Straightforward practice. Get the method working first.
4 problemsCo-interior with 125°, lines parallel. What is it?
Answer 55
Why 55°.
Vertical to 88°. What is it?
Answer 88
Why Equal.
Supplement of 88°?
Answer 92
Why 180 − 88.
Alternate interior to 37°, lines parallel. What is it?
Answer 37
Why Equal.
Build It Up
The same ideas with more to keep track of.
3 problemsCo-interior with 110°, lines parallel. What is it?
Answer 70
Why They add to 180.
How many different angle sizes appear at a transversal across parallel lines?
Answer 2
Why An angle and its supplement.
Sort each pair by its relationship when the lines are parallel.
Answer Equal: Corresponding angles, Alternate interior angles, Vertical angles · Add to 180°: Co-interior angles
Why Only one of the four is a supplementary pair.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsTwo angles on a straight line, one 3 times the other. What is the smaller?
Answer 45
Why x + 3x = 180.
Vertical angles are always equal. 1 for yes, 0 for no.
Answer 1
Why No parallel lines needed.
The Supplement: One angle is 65°. What is the angle beside it on a straight line?
Answer 115
Why 115°.
Corresponding: Corresponding angles with parallel lines. One is 42°. What is the other?
Answer 42
Why 42°.