Question Paper
Class / Subject: Class 9 (ICSE) · Mathematics
Chapter: Chapter 16 — Chapter 16: Area Theorems (Proof and Use)
Time Allowed: 32 minutes
Max Marks: 16
1. What is true about triangles with the same base and between the same parallels? [1]
(A) They have equal areas
(B) They have equal perimeters
(C) They are congruent
(D) They have no relationship
2. What is the relationship between a parallelogram and triangle sharing a base and parallels? [1]
(A) Parallelogram area = 2 × triangle area
(B) They have equal areas
(C) Triangle area = 2 × parallelogram area
(D) No relationship exists
3. What is used to prove these theorems? [1]
(A) Congruent triangle properties
(B) Only measurement, no proof needed
(C) Random guessing
(D) Nothing is used
4. Why are area theorems useful? [1]
(A) They allow area comparison without all measurements
(B) They have no use
(C) Only for decoration
(D) They complicate area calculation
5. Do triangles with the same base need to be the same shape for equal area? [1]
(A) No
(B) Yes, they must be identical
(C) Only isosceles triangles qualify
(D) This is impossible
6. What defines 'between the same parallels'? [1]
(A) Both figures lie within the same pair of parallel lines
(B) Both figures are identical
(C) Both figures share all sides
(D) Nothing specific
7. Why study area theorems? [1]
(A) To solve complex area problems efficiently
(B) No reason
(C) It's not useful
(D) Only for tests
8. What kind of figures do these theorems relate? [1]
(A) Triangles and parallelograms
(B) Only circles
(C) Only squares
(D) Only cubes
9. What is true about triangles with the same base and between the same parallels? [1]
(A) They have equal areas
(B) They have equal perimeters
(C) They are congruent
(D) They have no relationship
10. What is the relationship between a parallelogram and triangle sharing a base and parallels? [1]
(A) Parallelogram area = 2 × triangle area
(B) They have equal areas
(C) Triangle area = 2 × parallelogram area
(D) No relationship exists
11. What is used to prove these theorems? [1]
(A) Congruent triangle properties
(B) Only measurement, no proof needed
(C) Random guessing
(D) Nothing is used
12. Why are area theorems useful? [1]
(A) They allow area comparison without all measurements
(B) They have no use
(C) Only for decoration
(D) They complicate area calculation
13. Do triangles with the same base need to be the same shape for equal area? [1]
(A) No
(B) Yes, they must be identical
(C) Only isosceles triangles qualify
(D) This is impossible
14. What defines 'between the same parallels'? [1]
(A) Both figures lie within the same pair of parallel lines
(B) Both figures are identical
(C) Both figures share all sides
(D) Nothing specific
15. Why study area theorems? [1]
(A) To solve complex area problems efficiently
(B) No reason
(C) It's not useful
(D) Only for tests
16. What kind of figures do these theorems relate? [1]
(A) Triangles and parallelograms
(B) Only circles
(C) Only squares
(D) Only cubes