Geometry Similarity & Proportionality 2 — Questions and Answers
Question 1: Two triangles are similar with a scale factor of 3. If the smaller triangle has a perimeter of 12 cm, what is the perimeter of the larger triangle?
- 36 cm (Correct answer)
- 15 cm
- 108 cm
- 24 cm
Correct answer: 36 cm
Perimeter scales by the same factor as the sides, so 12 × 3 = 36 cm.
Question 2: In similar figures, the ratio of areas equals the ratio of corresponding sides:
- Squared (Correct answer)
- Equal to it
- Cubed
- Square-rooted
Correct answer: Squared
Area ratio is the square of the linear scale factor.
Question 3: A line parallel to one side of a triangle divides the other two sides proportionally. This is known as the:
- Triangle Proportionality Theorem (Correct answer)
- Pythagorean Theorem
- Angle Bisector Theorem
- Midsegment Theorem
Correct answer: Triangle Proportionality Theorem
The Triangle Proportionality (Basic Proportionality) Theorem states a parallel line cuts the sides proportionally.
Question 4: If two triangles have all three pairs of angles equal, they are guaranteed to be:
- Similar (Correct answer)
- Congruent
- Equilateral
- Right triangles
Correct answer: Similar
Equal corresponding angles (AA/AAA) guarantees similarity but not congruence.
Question 5: A 6 ft person casts a 4 ft shadow while a nearby tree casts a 20 ft shadow. How tall is the tree?
- 30 ft (Correct answer)
- 24 ft
- 13.3 ft
- 40 ft
Correct answer: 30 ft
Set up 6/4 = h/20, giving h = 30 ft.
Question 6: Which similarity criterion uses two pairs of proportional sides and the included angle?
- SAS similarity (Correct answer)
- AA similarity
- SSS similarity
- HL similarity
Correct answer: SAS similarity
SAS similarity requires two proportional sides with equal included angles.
Question 7: Two similar rectangles have a side ratio of 2:5. What is the ratio of their areas?
- 4:25 (Correct answer)
- 2:5
- 8:125
- 10:25
Correct answer: 4:25
Area ratio is the square of the side ratio: 2²:5² = 4:25.
Geometry Similarity & Proportionality 2
Two triangles are similar with a scale factor of 3.
If the smaller triangle has a perimeter of 12 cm, what is the perimeter of the larger triangle?