Cogito
Geometry · Chapter 4 · Lesson 2
Similar Figures and Scale
Same shape, proportional sides.
11 problems · about 23 minutes · G-SRT.A.2, G-SRT.B.5
What this lesson teaches
The student uses similarity to find unknown sides and compares areas.
- Similar figures have equal angles and sides in a constant ratio.
- Match corresponding sides by their position, not their appearance.
- Sides in ratio k put areas in ratio k².
Warm Up
Straightforward practice. Get the method working first.
4 problemsSides in ratio 4. Area ratio?
Answer 16
Why 16.
5 corresponds to 20. Scale factor?
Answer 4
Why 20 ÷ 5.
Factor 4. 3 corresponds to what?
Answer 12
Why 3 × 4.
Sides in ratio 2. What is the area ratio?
Answer 4
Why k².
Build It Up
The same ideas with more to keep track of.
3 problemsSides in ratio 3. What is the area ratio?
Answer 9
Why 3².
Do similar figures have equal angles? 1 for yes, 0 for no.
Answer 1
Why Same shape.
Do similar figures have equal sides? 1 for yes, 0 for no.
Answer 0
Why Proportional, not equal.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsAreas in ratio 25. What is the side ratio?
Answer 5
Why The square root.
Factor 0.5. Is the image smaller? 1 for yes, 0 for no.
Answer 1
Why Below one.
The Factor: 4 corresponds to 12. What is the scale factor?
Answer 3
Why 3.
The Missing Side: Same factor. 7 corresponds to what?
Answer 21
Why 21.