Try each question on your own first. Use the Show Answer button only after you have selected your option, then read the explanation and revise the related concept from your chapter notes.
9. Each angle of an equilateral triangle measures:
A. 45°
B. 90°
C. 60°
D. 30°
Answer: C. 60°
Explanation: All sides are equal in an equilateral triangle, so all 3 angles are equal: 180° / 3 = 60°.
10. RHS congruence criterion stands for:
A. Right angle - Hypotenuse - Side
B. Right angle - Height - Side
C. Ratio - Height - Side
D. Right angle - Horizontal - Side
Answer: A. Right angle - Hypotenuse - Side
Explanation: RHS criterion applies when two right-angled triangles have an equal hypotenuse and one equal side.
11. In ΔABC and ΔDEF, AB = FD and ∠A = ∠D. To make ΔABC ≅ ΔDFE by SAS criterion, which condition is required?
A. BC = EF
B. AC = DE
C. AC = EF
D. BC = DE
Answer: B. AC = DE
Explanation: For SAS with ∠A = ∠D, the sides including ∠A (AB, AC) must equal the sides including ∠D (DF, DE). Since AB = DF, AC must equal DE.
12. In ΔPQR, if ∠R > ∠Q, then:
A. QR > PR
B. PQ > PR
C. PQ < PR
D. QR < PQ
Answer: B. PQ > PR
Explanation: In any triangle, the side opposite to the larger angle is longer. Opposite to ∠R is PQ and opposite to ∠Q is PR, so PQ > PR.
13. In any triangle, the sum of any two sides is ________ the third side.
A. Less than
B. Equal to
C. Greater than
D. Half of
Answer: C. Greater than
Explanation: Triangle Inequality Property: The sum of the lengths of any two sides of a triangle is always greater than the third side.
14. In a right-angled triangle, which side is the longest side?
A. Perpendicular
B. Base
C. Hypotenuse
D. All sides are equal
Answer: C. Hypotenuse
Explanation: The right angle (90°) is the largest angle in a right triangle, so the side opposite to it (hypotenuse) is the longest.
15. If the three sides of a triangle are 4 cm, 5 cm, and 10 cm, can such a triangle be formed?
A. Yes
B. No
C. Only if it is a right triangle
D. Cannot be determined
Answer: B. No
Explanation: Sum of 4 + 5 = 9 cm, which is NOT greater than 10 cm. Since it violates the triangle inequality rule, no triangle can be formed.
16. If ΔABC ≅ ΔLMN, then which side is equal to MN?
A. AB
B. BC
C. AC
D. None of these
Answer: B. BC
Explanation: The vertex ordering is A↔L, B↔M, C↔N. Therefore, side BC corresponds to side MN.
17. In ΔABC, if ∠A = 40° and ∠B = 60°, which is the longest side?
A. AB
B. BC
C. AC
D. AB and BC are equal
Answer: A. AB
Explanation: ∠C = 180° - (40° + 60°) = 80°. Since ∠C is the largest angle, the side opposite to it (AB) is the longest side.
18. In ΔABC, if ∠A = 40° and ∠B = 60°, which is the shortest side?
A. AB
B. BC
C. AC
D. BC and AC are equal
Answer: B. BC
Explanation: ∠A = 40° is the smallest angle, so the side opposite to it (BC) is the shortest side.
19. If ΔPQR ≅ ΔEFD, then PR is equal to:
A. EF
B. FD
C. ED
D. QR
Answer: C. ED
Explanation: In ΔPQR ≅ ΔEFD, vertex P corresponds to E and R corresponds to D. Thus, PR = ED.
20. In an isosceles triangle ABC with AB = AC, if AD is a altitude to BC, then AD:
A. Bisects ∠A
B. Bisects BC
C. Both A and B
D. Neither A nor B
Answer: C. Both A and B
Explanation: The altitude drawn to the base of an isosceles triangle acts as both the angle bisector of vertex A and the perpendicular bisector of base BC.
21. The difference between any two sides of a triangle is ________ the third side.
A. Greater than
B. Equal to
C. Less than
D. Double of
Answer: C. Less than
Explanation: By triangle inequality properties, the difference between lengths of any two sides is always less than the third side.
22. If two sides of a triangle are 6 cm and 9 cm, the third side must lie between:
A. 3 cm and 15 cm
B. 6 cm and 9 cm
C. 0 cm and 15 cm
D. 3 cm and 9 cm
Answer: A. 3 cm and 15 cm
Explanation: Third side > (9 - 6 = 3 cm) and Third side < (9 + 6 = 15 cm).
23. In ΔABC, if ∠B = ∠C = 45°, then ΔABC is a/an:
A. Equilateral triangle
B. Isosceles right-angled triangle
C. Scalene triangle
D. Obtuse triangle
Answer: B. Isosceles right-angled triangle
Explanation: ∠A = 180° - (45° + 45°) = 90°. Since it has two equal angles (45°) and one right angle (90°), it is an isosceles right triangle.
24. What full form does 'CPCT' stand for?
A. Corresponding Parts of Congruent Triangles
B. Congruent Parts of Common Triangles
C. Corresponding Points of Congruent Triangles
D. Central Parts of Congruent Triangles
Answer: A. Corresponding Parts of Congruent Triangles
Explanation: CPCT stands for Corresponding Parts of Congruent Triangles.
25. In ΔABC, if AB = 5 cm, BC = 6 cm, and AC = 7 cm, which angle is the largest?
A. ∠A
B. ∠B
C. ∠C
D. All angles are equal
Answer: B. ∠B
Explanation: The side AC = 7 cm is the longest side, so the angle opposite to it (∠B) is the largest angle.
26. Of all line segments drawn to a given line from a point not lying on it, which is the shortest?
A. Slant line
B. Perpendicular line segment
C. Parallel line
D. Bisecting line
Answer: B. Perpendicular line segment
Explanation: The perpendicular line segment drawn from a point to a line is shorter than any other slant line segment drawn to that line.
27. If ΔABC ≅ ΔDEF and ∠A = 30°, ∠E = 70°, find ∠C.
This page contains a chapter-wise objective practice set. Try the questions without checking the answer first, then use the explanation to understand the point you missed. The current page contains 30 questions, so you can practise in smaller sets when you are revising.
Quick revision tip
After the practice set, write down the question numbers you missed and revise only those concepts once more. This makes MCQ practice more useful than repeatedly attempting the same questions without reviewing mistakes.
