Cogito
Grade 8 Math · Chapter 2 · Lesson 4
Angle-Angle Similarity
Two angles are enough.
10 problems · about 19 minutes · 8.G.A.5
What this lesson teaches
The child uses the angle sum and angle-angle criterion to decide whether triangles are similar.
- The angles of a triangle always add to 180°.
- Two matching angles force the third to match, so the triangles are similar.
- Similar triangles have proportional sides, not equal ones.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Dilations on the Coordinate Plane: (4, −3) dilated by 5. What is the new y?
Answer -15
Why (20, −15).
Review — Similar Figures: Similar figures. 4 matches 10. Another side is 6. Its match?
Answer 15
Why 15.
Review — Dilations: A side of 9 dilated by 3. New length?
Answer 27
Why 27.
Warm Up
Straightforward practice. Get the method working first.
3 problemsAngles 25° and 95°. What is the third?
Answer 60
Why 60°.
Angles 30° and 80°. What is the third?
Answer 70
Why 180 − 110.
Angles 90° and 45°. What is the third?
Answer 45
Why 180 − 135.
Build It Up
The same ideas with more to keep track of.
2 problemsDo similar triangles have equal side lengths? 1 for yes, 0 for no.
Answer 0
Why Proportional, not equal.
A triangle with angles 60, 60 and what?
Answer 60
Why They must total 180.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Third Angle: A triangle has angles 45° and 65°. What is the third, in degrees?
Answer 70
Why 70°.
The Criterion: How many matching angles are needed for similarity?
Answer 2
Why Two.