Similar Triangles Practice

Name:

Date:

📚 Part 1: Multiple Choice (choose one)

1. Triangle ABC has angles 30°, 60°, 90°. Triangle DEF has angles 60°, 30°, 90°. Are the triangles similar?

Yes — corresponding angles are equal

No — sides are different lengths

Not enough information

2. Triangles with side sets {3, 4, 5} and {6, 8, 10} are:

Similar (scale factor 2)

Congruent

Not similar

3. If ΔABC ∼ ΔDEF and AB corresponds to DE, BC corresponds to EF, AC corresponds to DF, the scale factor k = DE/AB. If AB = 7 cm and DE = 21 cm, what is k?

k = 1/3

k = 3

k = 14

4. Two triangles share one pair of equal acute angles but one other angle differs. Which statement is true?

The triangles are similar by AA

The triangles are not necessarily similar

They are congruent

✏️ Part 2: Short Answers & Applications

Success criteria: I can (1) identify when triangles are similar using AA or side ratios, (2) calculate the linear scale factor, (3) use that factor to find missing side lengths and area scale. Show working clearly.

Differentiation strategies: Support: provide a simple worked example and labelled diagram; Extension: solve a two-step problem involving perimeter and area scale factors; Visual learners: sketch triangles and mark corresponding sides; EAL/reading support: key vocabulary list (similar, corresponding, scale factor, ratio).

5. ΔABC ∼ ΔDEF with correspondence A→D, B→E, C→F. AB = 5 cm, BC = 7 cm, AC = 8 cm. DE = 15 cm. Find EF and DF (show units).

6. ΔABC ∼ ΔDEF (A→D, B→E, C→F). AB = 8 cm, AC = 12 cm. DE = 20 cm. Find DF. Give your answer in centimetres.

7. Explain in one or two sentences why triangles with angles 45°, 45°, 90° are always similar to each other.

8. If the linear scale factor from triangle T1 to triangle T2 is 3, and area of T1 is 20 cm², what is the area of T2? Show calculation and units.

9. Practical problem: A building casts a 12.0 m shadow at the same time a 2.0 m pole casts a 0.80 m shadow. Assume the sun's rays make similar triangles. Calculate the height of the building (in metres). Show steps.

10. Sketch two similar triangles (one larger, one smaller), label corresponding vertices and one pair of corresponding sides with lengths that show the scale factor. Explain the correspondence in one sentence.