Central Board of Secondary Education (CBSE - India) Class 9 Mathematics MCQs: Lines and Angles, Triangles, Quadrilaterals

Instructions. Answer all questions. Fill exactly one bubble per question on the OMR sheet.

1. Lines and Angles

   1.

   If two lines intersect, then the vertically opposite angles are always:

   1. (A)

      Equal

   2. (B)

      Unequal

   3. (C)

      Complementary

   4. (D)

      Supplementary

   Show answerHide answer

   Answer: (A)

   Equal

   Lines and Angles · Easy

2. 2.

   In the given figure, if $AB \| CD$ and $EF \perp CD$, and $\angle GED = 135^\circ$, find $\angle AFE$.

   1. (A)

      $150^\circ$

   2. (B)

      $45^\circ$

   3. (C)

      $135^\circ$

   4. (D)

      $90^\circ$

   Show answerHide answer

   Answer: (B)

   $45^\circ$

   Lines and Angles · Hard

3. 3.

   The sum of all angles around a point is:

   1. (A)

      $360^\circ$

   2. (B)

      $180^\circ$

   3. (C)

      $90^\circ$

   4. (D)

      $270^\circ$

   Show answerHide answer

   Answer: (A)

   $360^\circ$

   Lines and Angles · Easy

4. 4.

   If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are:

   1. (A)

      Complementary

   2. (B)

      Vertically opposite

   3. (C)

      Supplementary

   4. (D)

      Equal

   Show answerHide answer

   Answer: (C)

   Supplementary

   Lines and Angles · Medium

5. 5.

   An angle whose measure is greater than $90^\circ$ but less than $180^\circ$ is called a/an:

   1. (A)

      Reflex angle

   2. (B)

      Right angle

   3. (C)

      Obtuse angle

   4. (D)

      Acute angle

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   Answer: (C)

   Obtuse angle

   Lines and Angles · Easy

6. 6.

   If lines $l$ and $m$ are parallel, and a transversal $t$ intersects them such that $\angle 1 = 70^\circ$, then what is the measure of $\angle 8$?

   1. (A)

      $110^\circ$

   2. (B)

      $70^\circ$

   3. (C)

      $90^\circ$

   4. (D)

      $180^\circ$

   Show answerHide answer

   Answer: (B)

   $70^\circ$

   Lines and Angles · Medium

7. 7.

   If two angles are complementary, and one angle is $30^\circ$ more than the other, what are the measures of the angles?

   1. (A)

      $60^\circ, 30^\circ$

   2. (B)

      $30^\circ, 90^\circ$

   3. (C)

      $30^\circ, 60^\circ$

   4. (D)

      $40^\circ, 50^\circ$

   Show answerHide answer

   Answer: (C)

   $30^\circ, 60^\circ$

   Lines and Angles · Hard

8. 8.

   In $\triangle ABC$, if $AB = AC$ and $\angle A = 80^\circ$, then $\angle B$ is equal to:

   1. (A)

      $80^\circ$

   2. (B)

      $40^\circ$

   3. (C)

      $50^\circ$

   4. (D)

      $100^\circ$

   Show answerHide answer

   Answer: (C)

   $50^\circ$

   Lines and Angles · Medium

9. 9.

   If two angles form a linear pair and one of them is an acute angle, then the other angle must be a/an:

   1. (A)

      Acute angle

   2. (B)

      Obtuse angle

   3. (C)

      Reflex angle

   4. (D)

      Right angle

   Show answerHide answer

   Answer: (B)

   Obtuse angle

   Lines and Angles · Medium

10. 10.

    In the given figure, if $POQ$ is a line, the value of $x$ for which $AOB$ is a straight line is:

    1. (A)

       $30^\circ$

    2. (B)

       $20^\circ$

    3. (C)

       $50^\circ$

    4. (D)

       $40^\circ$

    Show answerHide answer

    Answer: (A)

    $30^\circ$

    Lines and Angles · Hard

11. Triangles

    11.

    Which of the following is not a criterion for congruence of triangles?

    1. (A)

       SAS (Side-Angle-Side)

    2. (B)

       ASA (Angle-Side-Angle)

    3. (C)

       SSA (Side-Side-Angle)

    4. (D)

       RHS (Right angle-Hypotenuse-Side)

    Show answerHide answer

    Answer: (C)

    SSA (Side-Side-Angle)

    Triangles · Easy

12. 12.

    If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent by which rule?

    1. (A)

       SAS congruence rule

    2. (B)

       SSS congruence rule

    3. (C)

       RHS congruence rule

    4. (D)

       ASA congruence rule

    Show answerHide answer

    Answer: (D)

    ASA congruence rule

    Triangles · Easy

13. 13.

    In $\triangle ABC$, if $AB=AC$ and $\angle B = 50^\circ$, then $\angle C$ is equal to:

    1. (A)

       $40^\circ$

    2. (B)

       $130^\circ$

    3. (C)

       $50^\circ$

    4. (D)

       $80^\circ$

    Show answerHide answer

    Answer: (C)

    $50^\circ$

    Triangles · Easy

14. 14.

    In $\triangle PQR$, if $\angle P = 60^\circ$ and $\angle Q = 70^\circ$, then $\angle R$ is:

    1. (A)

       $130^\circ$

    2. (B)

       $50^\circ$

    3. (C)

       $60^\circ$

    4. (D)

       $70^\circ$

    Show answerHide answer

    Answer: (B)

    $50^\circ$

    Triangles · Easy

15. 15.

    If $\triangle ABC \cong \triangle PQR$ by SAS congruence rule, then which of the following is true?

    1. (A)

       $AB=PQ$, $\angle B=\angle Q$, $BC=QR$

    2. (B)

       $AB=PQ$, $\angle A=\angle P$, $AC=PR$

    3. (C)

       $AC=PR$, $\angle B=\angle Q$, $BC=QR$

    4. (D)

       $BC=QR$, $\angle C=\angle R$, $AC=PR$

    Show answerHide answer

    Answer: (A)

    $AB=PQ$, $\angle B=\angle Q$, $BC=QR$

    Triangles · Medium

16. 16.

    In an isosceles triangle, if the vertical angle is $100^\circ$, what is the measure of each base angle?

    1. (A)

       $50^\circ$

    2. (B)

       $40^\circ$

    3. (C)

       $80^\circ$

    4. (D)

       $100^\circ$

    Show answerHide answer

    Answer: (B)

    $40^\circ$

    Triangles · Medium

17. 17.

    In $\triangle ABC$, $AB=AC$. If $\angle A = 80^\circ$, then $\angle B$ is:

    1. (A)

       $50^\circ$

    2. (B)

       $70^\circ$

    3. (C)

       $60^\circ$

    4. (D)

       $100^\circ$

    Show answerHide answer

    Answer: (A)

    $50^\circ$

    Triangles · Medium

18. 18.

    Which statement is true for an equilateral triangle?

    1. (A)

       Only two sides are equal.

    2. (B)

       All angles are $60^\circ$.

    3. (C)

       One angle is $90^\circ$.

    4. (D)

       All sides are different.

    Show answerHide answer

    Answer: (B)

    All angles are $60^\circ$.

    Triangles · Easy

19. 19.

    In $\triangle XYZ$, if $\angle X = 90^\circ$ and $XY=YZ$, then $\angle Y$ is:

    1. (A)

       $90^\circ$

    2. (B)

       $30^\circ$

    3. (C)

       $45^\circ$

    4. (D)

       $60^\circ$

    Show answerHide answer

    Answer: (C)

    $45^\circ$

    Triangles · Medium

20. 20.

    If two sides of a triangle are $6 \text{ cm}$ and $10 \text{ cm}$, the third side cannot be:

    1. (A)

       $12 \text{ cm}$

    2. (B)

       $4 \text{ cm}$

    3. (C)

       $8 \text{ cm}$

    4. (D)

       $15 \text{ cm}$

    Show answerHide answer

    Answer: (B)

    $4 \text{ cm}$

    Triangles · Hard

21. 21.

    In $\triangle ABC$, if $\angle A > \angle B$, then which of the following is true?

    1. (A)

       $AC = BC$

    2. (B)

       $AC > BC$

    3. (C)

       $AB > BC$

    4. (D)

       $BC > AC$

    Show answerHide answer

    Answer: (D)

    $BC > AC$

    Triangles · Medium

22. 22.

    If $AD$ is the median of $\triangle ABC$ and $AD=BD=CD$, then $\angle BAC$ is:

    1. (A)

       $120^\circ$

    2. (B)

       $90^\circ$

    3. (C)

       $60^\circ$

    4. (D)

       $180^\circ$

    Show answerHide answer

    Answer: (B)

    $90^\circ$

    Triangles · Hard

23. 23.

    In a right-angled triangle, if one acute angle is double the other, what are the measures of the acute angles?

    1. (A)

       $45^\circ, 45^\circ$

    2. (B)

       $30^\circ, 60^\circ$

    3. (C)

       $20^\circ, 40^\circ$

    4. (D)

       $10^\circ, 20^\circ$

    Show answerHide answer

    Answer: (B)

    $30^\circ, 60^\circ$

    Triangles · Medium

24. 24.

    Given $\triangle PQR$ and $\triangle LMN$ with $PQ=LM$, $\angle P=\angle L$, and $QR=MN$. Which congruence rule applies?

    1. (A)

       ASA

    2. (B)

       SAS

    3. (C)

       SSS

    4. (D)

       None of these can guarantee congruence

    Show answerHide answer

    Answer: (D)

    None of these can guarantee congruence

    Triangles · Hard

25. 25.

    In $\triangle ABC$, $AB = 5 \text{ cm}$, $BC = 8 \text{ cm}$, and $AC = 7 \text{ cm}$. Which angle is the smallest?

    1. (A)

       $\angle C$

    2. (B)

       $\angle B$

    3. (C)

       $\angle A$

    4. (D)

       Cannot be determined

    Show answerHide answer

    Answer: (A)

    $\angle C$

    Triangles · Medium

26. 26.

    If $E$ and $F$ are the midpoints of sides $AC$ and $AB$ respectively of $\triangle ABC$, and $BE=CF$, then $\triangle ABC$ is an isosceles triangle. This is based on which congruence criterion?

    1. (A)

       ASA

    2. (B)

       RHS

    3. (C)

       SAS

    4. (D)

       SSS

    Show answerHide answer

    Answer: (C)

    SAS

    Triangles · Hard

27. 27.

    In $\triangle PQR$, if $\angle P = 2\angle Q$ and $QR = PR$, then the measure of $\angle R$ is:

    1. (A)

       $72^\circ$

    2. (B)

       $108^\circ$

    3. (C)

       $144^\circ$

    4. (D)

       $36^\circ$

    Show answerHide answer

    Answer: (B)

    $108^\circ$

    Triangles · Hard

28. 28.

    Two triangles are congruent if two angles and a non-included side of one triangle are equal to the corresponding angles and non-included side of the other triangle. This is known as:

    1. (A)

       SSS congruence rule

    2. (B)

       SAS congruence rule

    3. (C)

       AAS congruence rule

    4. (D)

       ASA congruence rule

    Show answerHide answer

    Answer: (C)

    AAS congruence rule

    Triangles · Easy

29. 29.

    The sum of any two sides of a triangle is always:

    1. (A)

       greater than the third side

    2. (B)

       equal to the third side

    3. (C)

       double the third side

    4. (D)

       less than the third side

    Show answerHide answer

    Answer: (A)

    greater than the third side

    Triangles · Easy

30. 30.

    In $\triangle ABC$, $AD$ is perpendicular to $BC$. If $BD=CD$, then $\triangle ABD \cong \triangle ACD$ by which congruence rule?

    1. (A)

       SAS

    2. (B)

       ASA

    3. (C)

       RHS

    4. (D)

       SSS

    Show answerHide answer

    Answer: (A)

    SAS

    Triangles · Medium

31. Quadrilaterals

    31.

    The sum of all interior angles of a quadrilateral is:

    1. (A)

       $720^\circ$

    2. (B)

       $360^\circ$

    3. (C)

       $180^\circ$

    4. (D)

       $90^\circ$

    Show answerHide answer

    Answer: (B)

    $360^\circ$

    Quadrilaterals · Easy

32. 32.

    If the diagonals of a quadrilateral bisect each other, then it is a:

    1. (A)

       Parallelogram

    2. (B)

       Rhombus

    3. (C)

       Kite

    4. (D)

       Trapezium

    Show answerHide answer

    Answer: (A)

    Parallelogram

    Quadrilaterals · Medium

33. 33.

    In a parallelogram ABCD, if $\angle A = 75^\circ$, then $\angle B$ is:

    1. (A)

       $90^\circ$

    2. (B)

       $75^\circ$

    3. (C)

       $115^\circ$

    4. (D)

       $105^\circ$

    Show answerHide answer

    Answer: (D)

    $105^\circ$

    Quadrilaterals · Medium

34. 34.

    A quadrilateral having exactly one pair of parallel sides is called a:

    1. (A)

       Rhombus

    2. (B)

       Trapezium

    3. (C)

       Rectangle

    4. (D)

       Parallelogram

    Show answerHide answer

    Answer: (B)

    Trapezium

    Quadrilaterals · Easy

35. 35.

    Which of the following statements is true for a square?

    1. (A)

       Diagonals bisect each other but are not equal.

    2. (B)

       Diagonals are equal but not perpendicular.

    3. (C)

       Diagonals are perpendicular bisectors of each other.

    4. (D)

       Diagonals do not bisect each other.

    Show answerHide answer

    Answer: (C)

    Diagonals are perpendicular bisectors of each other.

    Quadrilaterals · Medium

36. 36.

    The angles of a quadrilateral are in the ratio $3:5:9:13$. The smallest angle is:

    1. (A)

       $30^\circ$

    2. (B)

       $54^\circ$

    3. (C)

       $45^\circ$

    4. (D)

       $36^\circ$

    Show answerHide answer

    Answer: (D)

    $36^\circ$

    Quadrilaterals · Hard

37. 37.

    If in a parallelogram ABCD, $\angle D = 135^\circ$, then the measure of $\angle B$ is:

    1. (A)

       $45^\circ$

    2. (B)

       $75^\circ$

    3. (C)

       $135^\circ$

    4. (D)

       $90^\circ$

    Show answerHide answer

    Answer: (C)

    $135^\circ$

    Quadrilaterals · Easy

38. 38.

    The figure formed by joining the midpoints of the sides of a rhombus, in order, is a:

    1. (A)

       Rectangle

    2. (B)

       Parallelogram

    3. (C)

       Square

    4. (D)

       Rhombus

    Show answerHide answer

    Answer: (A)

    Rectangle

    Quadrilaterals · Hard

39. 39.

    In a quadrilateral ABCD, if AC and BD are diagonals, then:

    1. (A)

       $AB+BC+CD+DA = AC+BD$

    2. (B)

       $AB+BC+CD+DA = 2(AC+BD)$

    3. (C)

       $AB+BC+CD+DA < AC+BD$

    4. (D)

       $AB+BC+CD+DA > AC+BD$

    Show answerHide answer

    Answer: (D)

    $AB+BC+CD+DA > AC+BD$

    Quadrilaterals · Hard

40. 40.

    A diagonal of a parallelogram divides it into two congruent:

    1. (A)

       Triangles

    2. (B)

       Trapeziums

    3. (C)

       Rectangles

    4. (D)

       Rhombuses

    Show answerHide answer

    Answer: (A)

    Triangles

    Quadrilaterals · Easy

41. 41.

    If all angles of a quadrilateral are equal, then each angle is:

    1. (A)

       $180^\circ$

    2. (B)

       $90^\circ$

    3. (C)

       $60^\circ$

    4. (D)

       $45^\circ$

    Show answerHide answer

    Answer: (B)

    $90^\circ$

    Quadrilaterals · Easy

42. 42.

    A quadrilateral whose diagonals are equal and bisect each other at right angles is a:

    1. (A)

       Rectangle

    2. (B)

       Rhombus

    3. (C)

       Parallelogram

    4. (D)

       Square

    Show answerHide answer

    Answer: (D)

    Square

    Quadrilaterals · Medium

43. 43.

    The consecutive angles of a parallelogram are in the ratio $1:3$. The smallest angle is:

    1. (A)

       $30^\circ$

    2. (B)

       $45^\circ$

    3. (C)

       $60^\circ$

    4. (D)

       $90^\circ$

    Show answerHide answer

    Answer: (B)

    $45^\circ$

    Quadrilaterals · Hard

44. 44.

    In a parallelogram ABCD, if $AB=5$ cm and $BC=7$ cm, then the perimeter is:

    1. (A)

       $12$ cm

    2. (B)

       $24$ cm

    3. (C)

       $14$ cm

    4. (D)

       $10$ cm

    Show answerHide answer

    Answer: (B)

    $24$ cm

    Quadrilaterals · Medium

45. 45.

    Which of the following is not a property of a parallelogram?

    1. (A)

       Opposite sides are equal.

    2. (B)

       Diagonals bisect each other.

    3. (C)

       Opposite angles are equal.

    4. (D)

       Diagonals are perpendicular.

    Show answerHide answer

    Answer: (D)

    Diagonals are perpendicular.

    Quadrilaterals · Medium

46. 46.

    If one angle of a parallelogram is $90^\circ$, then it is a:

    1. (A)

       Trapezium

    2. (B)

       Rectangle

    3. (C)

       Square

    4. (D)

       Rhombus

    Show answerHide answer

    Answer: (B)

    Rectangle

    Quadrilaterals · Easy

47. 47.

    In a quadrilateral ABCD, $AB || CD$ and $AD=BC$. This quadrilateral is a:

    1. (A)

       Rhombus

    2. (B)

       Kite

    3. (C)

       Isosceles trapezium

    4. (D)

       Parallelogram

    Show answerHide answer

    Answer: (C)

    Isosceles trapezium

    Quadrilaterals · Medium

48. 48.

    The midpoints of the sides of a quadrilateral ABCD are P, Q, R, S respectively. If AC = 8 cm and BD = 6 cm, then the perimeter of PQRS is:

    1. (A)

       $28$ cm

    2. (B)

       $14$ cm

    3. (C)

       $7$ cm

    4. (D)

       $24$ cm

    Show answerHide answer

    Answer: (B)

    $14$ cm

    Quadrilaterals · Hard

49. 49.

    If angles A, B, C, D of a quadrilateral are in the ratio $1:2:3:4$, then the largest angle is:

    1. (A)

       $108^\circ$

    2. (B)

       $72^\circ$

    3. (C)

       $144^\circ$

    4. (D)

       $36^\circ$

    Show answerHide answer

    Answer: (C)

    $144^\circ$

    Quadrilaterals · Hard

50. 50.

    A quadrilateral in which all four sides are equal is a:

    1. (A)

       Trapezium

    2. (B)

       Rhombus

    3. (C)

       Rectangle

    4. (D)

       Parallelogram

    Show answerHide answer

    Answer: (B)

    Rhombus

    Quadrilaterals · Easy

— End of the paper · updated 13 November 2026 —