Similar Figures Quiz

Name:

Date:

📚 Part 1: Multiple Choice

I can: Identify similar figures and use scale factors to find missing lengths, perimeters, and areas.

Success Criteria: Show correct scale factor work, label corresponding sides, and compute perimeter/area changes.

1. Triangles A and B are similar. Triangle A has sides 3, 4, 5. The side corresponding to 3 in triangle B is 6. What is the scale factor from A to B?

1/2

2. Two rectangles are similar. Rectangle 1 measures 4 in by 7 in. Rectangle 2 has a corresponding side to 4 in that is 10 in. What is the missing corresponding side length?

14 in

17.5 in

20 in

35 in

3. If the scale factor from figure A to figure B is 3, the area of B compared to A is:

3 times

6 times

9 times

27 times

4. Two similar polygons have a scale factor of 1.5 from small to large. If the small polygon's perimeter is 24 ft, the large perimeter is:

32 ft

36 ft

30 ft

28 ft

✏️ Part 2: Short Answers & Work

5. Triangle A has sides 5, 12, 13. Triangle B is similar and the side corresponding to 12 is 18. Find the scale factor (A → B) and the lengths of the other two sides of B.

6. A right triangle has legs 8 and 15 (hypotenuse 17). A similar triangle has the leg corresponding to 8 equal to 24. Find the scale factor and the hypotenuse of the larger triangle.

7. A small rectangle has area 20 in². A similar larger rectangle has linear scale factor 3 (small → large). What is the area of the larger rectangle?

8. If the ratio of perimeters of two similar figures is 5:8, what is the ratio of their areas? Show your reasoning.

📌 Teacher Notes & Supports

Differentiation Strategies: Provide step-by-step guided notes, let students use graph paper or physical models, and offer calculators for area calculations if needed.

Extension Activities: Ask advanced learners to prove area ratio rules for similar figures or explore similarity in 3D (scale factor effects on surface area and volume).

Dyslexia-friendly Options: Offer a read-aloud of questions, highlight keywords (scale factor, corresponding, area, perimeter), increase line spacing, and present one problem at a time.

Reminder: Show all work and label corresponding sides when finding scale factors.