This revision of Chapter 7: Triangles (Class 9 Maths) is all about active practice. MCQs will push you to apply concepts like SSS, SAS, and RHS, while fill-in-the-blanks will sharpen your recall of theorems and important details. Every answer is included, so you’ll know instantly where you stand.
Class 9th Maths Important MCQs with Answers from Chapter 7 – Triangles
Question 1. Two triangles are congruent if their shapes and sizes are ___.
a) Different
b) Same
c) Similar only
d) Unequal
Answer:
b) Same – Congruent triangles are identical in shape and size.
Question 2. If ∆ABC ≅ ∆PQR, then the correct correspondence is:
a) A ↔ Q, B ↔ P, C ↔ R
b) A ↔ P, B ↔ Q, C ↔ R
c) A ↔ R, B ↔ Q, C ↔ P
d) A ↔ P, B ↔ R, C ↔ Q
Answer:
b) A ↔ P, B ↔ Q, C ↔ R – The order of vertices must be preserved.
Question 3. CPCT stands for:
a) Corresponding points of congruent triangles
b) Corresponding parts of congruent triangles
c) Congruent pairs of corresponding triangles
d) Congruent points of common triangles
Answer:
b) Corresponding parts of congruent triangles.
Question 4. Which of the following is NOT a valid congruence rule?
a) SAS
b) ASA
c) AAS
d) SSA
Answer:
d) SSA – This does not guarantee triangle congruence.
Question 5. Two right triangles are congruent if the hypotenuse and one side are equal. This is called:
a) SAS rule
b) RHS rule
c) ASA rule
d) SSS rule
Answer:
b) RHS rule – Right angle, Hypotenuse, and one Side.
Question 6. If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent by:
a) ASA rule
b) SAS rule
c) AAS rule
d) RHS rule
Answer:
b) SAS rule.
Question 7. If two angles and the included side of one triangle are equal to the corresponding two angles and included side of another, they are congruent by:
a) SAS
b) ASA
c) AAS
d) RHS
Answer:
b) ASA rule.
Question 8. If two angles and one corresponding side of a triangle are equal to two angles and corresponding side of another, the triangles are congruent by:
a) AAS
b) SAS
c) RHS
d) SSS
Answer:
a) AAS rule.
Question 9. If three sides of one triangle are equal to the three sides of another triangle, the triangles are congruent by:
a) SSS rule
b) ASA rule
c) AAS rule
d) SAS rule
Answer:
a) SSS rule.
Question 10. In an isosceles triangle, the angles opposite to the equal sides are:
a) Unequal
b) Equal
c) Supplementary
d) Complementary
Answer:
b) Equal.
Question 11. The converse of the isosceles triangle theorem states: If two angles of a triangle are equal, then the ___ opposite to them are equal.
a) Vertices
b) Sides
c) Medians
d) Heights
Answer:
b) Sides.
Question 12. In an equilateral triangle, each angle measures:
a) 30°
b) 45°
c) 60°
d) 90°
Answer:
c) 60°.
Question 13. Which of the following pairs of triangles are always congruent?
a) Two right triangles with equal hypotenuse and one equal side
b) Two right triangles with equal hypotenuse only
c) Two triangles with three equal angles
d) Two isosceles triangles with equal base angles
Answer:
a) Two right triangles with equal hypotenuse and one equal side.
Question 14. Which criterion is used in proving that diagonals of a rhombus bisect each other at right angles?
a) ASA rule
b) RHS rule
c) SAS rule
d) AAS rule
Answer:
c) SAS rule.
Question 15. In ∆ABC, if AB = AC, then which property holds true?
a) ∠B = ∠C
b) ∠A = ∠B
c) ∠A = ∠C
d) ∠A = ∠B = ∠C
Answer:
a) ∠B = ∠C.
Question 16. In ∆PQR, if ∆PQR ≅ ∆ABC and PQ = 5 cm, then AB = ___.
a) 4 cm
b) 5 cm
c) 6 cm
d) Cannot be determined
Answer:
b) 5 cm – CPCT applies.
Question 17. Which congruence rule is applied when proving two altitudes of an isosceles triangle are equal?
a) SSS
b) SAS
c) ASA
d) RHS
Answer:
d) RHS – Right triangles formed with altitudes.
Question 18. If ∆ABC ≅ ∆DEF, then ∠A corresponds to:
a) ∠F
b) ∠D
c) ∠E
d) ∠B
Answer:
b) ∠D.
Question 19. The line joining the mid-points of two sides of a triangle is ___ to the third side.
a) Perpendicular
b) Parallel
c) Equal
d) Unequal
Answer:
b) Parallel.
Question 20. If two medians of two triangles are equal and corresponding sides are equal, then the triangles are:
a) Not congruent
b) Similar only
c) Congruent
d) Unequal
Answer:
c) Congruent.
Question 21. In a triangle, the largest side is opposite the ___ angle.
a) Smallest
b) Largest
c) Right
d) Equal
Answer:
b) Largest.
Question 22. In a triangle, if two sides are unequal, then the longer side is opposite the ___ angle.
a) Smaller
b) Larger
c) Right
d) Reflex
Answer:
b) Larger.
Question 23. If in a triangle, one angle is greater than another, then the side opposite the greater angle is ___.
a) Smaller
b) Larger
c) Equal
d) Reflex
Answer:
b) Larger.
Question 24. In ∆ABC, if ∠A = 40°, ∠B = 60°, then ∠C = ___.
a) 60°
b) 80°
c) 100°
d) 120°
Answer:
c) 80° – Sum of angles in triangle = 180°.
Question 25. The sum of all three angles of a triangle is always ___.
a) 90°
b) 120°
c) 180°
d) 360°
Answer:
c) 180°.
Question 26. Which congruence rule is most often applied in proving two diagonals bisect each other in a parallelogram?
a) ASA
b) SAS
c) RHS
d) AAS
Answer:
b) SAS.
Question 27. An equilateral triangle has all three sides equal and all three angles equal to ___.
a) 30°
b) 45°
c) 60°
d) 90°
Answer:
c) 60°.
Question 28. In an isosceles triangle, if one base angle is 70°, then the other base angle is ___.
a) 40°
b) 50°
c) 70°
d) 80°
Answer:
c) 70°.
Question 29. Which theorem states that angles opposite equal sides of an isosceles triangle are equal?
a) Theorem 7.1
b) Theorem 7.2
c) Theorem 7.3
d) Theorem 7.4
Answer:
b) Theorem 7.2.
Question 30. The converse of Theorem 7.2 is given by:
a) Angles opposite equal sides are equal
b) Sides opposite equal angles are equal
c) All angles are 60°
d) CPCT is valid
Answer:
b) Sides opposite equal angles are equal.
Question 31. The perpendicular bisector of a line segment is the locus of points equidistant from the segment’s ___.
a) Midpoints
b) Endpoints
c) Altitudes
d) Medians
Answer:
b) Endpoints.
Question 32. If a line bisects an angle of a triangle, the point on the line is ___ from the arms of the angle.
a) Unequal
b) Equidistant
c) Parallel
d) Perpendicular
Answer:
b) Equidistant.
Question 33. In ∆PQR, if ∠P > ∠Q, then side opposite ∠P is ___ than side opposite ∠Q.
a) Smaller
b) Equal
c) Larger
d) Reflex
Answer:
c) Larger.
Question 34. Which rule proves congruence between two right triangles with hypotenuse 10 cm and one leg 6 cm equal?
a) ASA
b) SAS
c) RHS
d) SSS
Answer:
c) RHS – Hypotenuse and one side are equal.
Question 35. A triangle with all sides equal is called ___.
a) Scalene
b) Isosceles
c) Equilateral
d) Right-angled
Answer:
c) Equilateral.
Fill in the blanks on Triangles for Class 9 Maths
1. Two triangles are said to be ___ if they are equal in shape and size.
Answer:
congruent
2. The full form of CPCT is ___.
Answer:
Corresponding Parts of Congruent Triangles
3. The criterion of congruence in which two sides and the included angle are equal is called the ___ rule.
Answer:
SAS
4. If two angles and the included side of one triangle are equal to the corresponding parts of another triangle, the triangles are congruent by the ___ rule.
Answer:
ASA
5. If two angles and one corresponding side are equal in two triangles, they are congruent by the ___ rule.
Answer:
AAS
6. Two right triangles are congruent if the hypotenuse and one side are equal. This is known as the ___ rule.
Answer:
RHS
7. If three sides of one triangle are equal to the three sides of another, the triangles are congruent by the ___ rule.
Answer:
SSS
8. In an isosceles triangle, the angles opposite to the equal sides are always ___.
Answer:
equal
9. The converse of the isosceles triangle theorem states that if two angles of a triangle are equal, the sides opposite to them are ___.
Answer:
equal
10. Each angle of an equilateral triangle measures ___.
Answer:
60°
11. In a triangle, the largest side is always opposite the ___ angle.
Answer:
largest
12. In a triangle, if one angle is greater than another, the side opposite the greater angle is ___ than the side opposite the smaller angle.
Answer:
longer
13. The sum of the three angles of a triangle is always ___.
Answer:
180°
14. A triangle with no two sides equal is called a ___ triangle.
Answer:
scalene
15. A triangle with two sides equal is called an ___ triangle.
Answer:
isosceles
16. A triangle with all three sides equal is called an ___ triangle.
Answer:
equilateral
17. If in a triangle ∠A = 40° and ∠B = 60°, then ∠C = ___.
Answer:
80°
18. In a right-angled triangle, the side opposite the right angle is called the ___.
Answer:
hypotenuse
19. The perpendicular bisector of a line segment is the locus of points equidistant from the ___ of the segment.
Answer:
endpoints
20. If a line bisects an angle of a triangle, then the point on that line is ___ from the arms of the angle.
Answer:
equidistant
21. If ∆ABC ≅ ∆DEF and AB = 5 cm, then the corresponding side DE = ___.
Answer:
5 cm
22. If ∆ABC ≅ ∆DEF, then ∠A corresponds to ∠___.
Answer:
D
23. In an isosceles triangle, if each base angle is 70°, then the vertex angle is ___.
Answer:
40°
24. In an equilateral triangle of side 6 cm, the measure of each altitude is ___ cm.
Answer:
3√3 cm
25. The inequality property of triangles states that the sum of the lengths of any two sides of a triangle is always ___ than the third side.
Answer:
greater
