Cogito
Grade 8 Math · Chapter 2 · Lesson 2
Similar Figures
Same shape, different size.
10 problems · about 19 minutes · 8.G.A.4, 8.G.A.5
What this lesson teaches
The child decides whether figures are similar and uses similarity to find missing lengths.
- Similar means rigid motions plus a dilation carry one onto the other.
- Matching angles are equal and matching sides share one ratio.
- Two equal angles make triangles similar.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Dilations: A side of 9 dilated by 3. New length?
Answer 27
Why 27.
Review — Sequences of Moves: Rotated 90° three times. Total turn in degrees?
Answer 270
Why 270°.
Warm Up
Straightforward practice. Get the method working first.
4 problemsSimilar figures. 4 matches 10. Another side is 6. Its match?
Answer 15
Why 15.
What is true of similar figures?
Answer Equal angles and sides in one ratio.
Why Angles equal, sides proportional.
Similar figures. 2 matches 8. Another side is 5. Its match?
Answer 20
Why Factor 4.
Similar figures. 6 matches 9. Another side is 4. Its match?
Answer 6
Why Factor 1.5.
Build It Up
The same ideas with more to keep track of.
2 problemsTwo triangles share angles of 50 and 60. Are they similar?
Answer Yes.
Why Two angles is enough.
Similar figures. 5 matches 15. Another side is 7. Its match?
Answer 21
Why Factor 3.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Similar Pair: Similar triangles. 3 matches 12, and another side is 5. What is its match?
Answer 20
Why 20.
The Angles: Two similar triangles. One angle is 63 degrees. What is the matching angle?
Answer 63 degrees
Why 63 degrees.