Chapter-11 Similarity and Congruence — Online MCQ Test
MATHS · Grade 10 · IGCSE cambridge
Practice Chapter-11 Similarity and Congruence with a free chapter-wise online MCQ test.
This chapter covers: Similar shapes scale factors for length area and volume and conditions for congruent triangles..
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Chapter-11 Similarity and Congruence — Important Questions & Answers
Two triangles are congruent. Which of the following is NOT a sufficient condition for congruence?
- A. SSS (Side-Side-Side)
- B. SAS (Side-Angle-Side)
- C. AAA (Angle-Angle-Angle)
- D. RHS (Right angle-Hypotenuse-Side)
Answer: C. AAA (Angle-Angle-Angle)
AAA proves similarity, not congruence. Two triangles with equal angles can have different sizes. SSS, SAS, and RHS all guarantee congruence.
AAA proves similarity, not congruence. Two triangles with equal angles can have different sizes. SSS, SAS, and RHS all guarantee congruence.
What does a scale factor of 2 mean when comparing two similar shapes?
- A. All linear dimensions of the larger shape are twice those of the smaller shape
- B. The area of the larger shape is twice that of the smaller shape
- C. The perimeter is half of the original
- D. The volume increases by a factor of 2
Answer: A. All linear dimensions of the larger shape are twice those of the smaller shape
A scale factor of 2 for length means all linear dimensions (sides, heights, widths) are multiplied by 2. Area scales by 2², and volume by 2³.
A scale factor of 2 for length means all linear dimensions (sides, heights, widths) are multiplied by 2. Area scales by 2², and volume by 2³.
Two similar triangles have corresponding sides in the ratio 2:5. If the smaller triangle has a perimeter of 24 cm, what is the perimeter of the larger triangle?
- A. 60 cm
- B. 48 cm
- C. 96 cm
- D. 120 cm
Answer: A. 60 cm
The perimeter scales by the same factor as the sides. If sides are in ratio 2:5, then perimeters are also in ratio 2:5. Therefore, 24 × (5/2) = 60 cm.
The perimeter scales by the same factor as the sides. If sides are in ratio 2:5, then perimeters are also in ratio 2:5. Therefore, 24 × (5/2) = 60 cm.
Which of the following is a condition that guarantees congruence of two right-angled triangles?
- A. Two angles are equal
- B. One leg and the hypotenuse are respectively equal to one leg and hypotenuse of the other triangle
- C. The hypotenuses are equal
- D. Two legs are equal in length
Answer: B. One leg and the hypotenuse are respectively equal to one leg and hypotenuse of the other triangle
The RHS (Right angle-Hypotenuse-Side) condition states that if the hypotenuse and one leg of a right triangle equal the hypotenuse and one leg of another right triangle, they are congruent.
The RHS (Right angle-Hypotenuse-Side) condition states that if the hypotenuse and one leg of a right triangle equal the hypotenuse and one leg of another right triangle, they are congruent.
Two cubes have a linear scale factor of 2:3. The smaller cube has a volume of 64 cm³. What is the volume of the larger cube, and by what factor does the volume increase?
- A. 144 cm³; factor of 1.5
- B. 216 cm³; factor of 3.375
- C. 192 cm³; factor of 2.25
- D. 288 cm³; factor of 4.5
Answer: B. 216 cm³; factor of 3.375
Linear scale factor 2:3 means volume scale factor is (2:3)³ = 8:27. Volume of larger cube = 64 × (27/8) = 216 cm³. The volume increases by factor 27/8 = 3.375.
Linear scale factor 2:3 means volume scale factor is (2:3)³ = 8:27. Volume of larger cube = 64 × (27/8) = 216 cm³. The volume increases by factor 27/8 = 3.375.