AmbifulWorksheets
Practice that never repeats
CBSE · Class 9 · Mathematics

Propositions and their Converses

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
A proposition is a statement that is:
  1. a question
  2. an opinion
  3. always true
  4. either true or false, but not both
2.
The converse of 'If two sides of a triangle are equal, then the angles opposite them are equal.' is:
  1. If two angles of a triangle are equal, then the sides opposite them are equal.
  2. If two sides of a triangle are equal, then the angles opposite them are equal.
  3. If a2 = b2, then a = b.
  4. If x2 = 9, then x = 3.
3.
A triangle has sides 80 cm, 84 cm and 116 cm. It is:
  1. acute-angled
  2. not a triangle
  3. obtuse-angled
  4. right-angled
4.
In △ABC, ∠B = ∠C = 43° and AB = 6 cm. Then AC =
  1. 8 cm
  2. 12 cm
  3. 6 cm
  4. cannot be found
5.
Which number is a counterexample to 'If a number is divisible by 5, then it is divisible by 15'?
  1. 50
  2. 90
  3. 75
  4. 120
6.
Which test tells us two lines are parallel?
  1. equal distances at one point only
  2. equal lengths
  3. a right angle at one end
  4. equal corresponding angles made by a transversal
7.
In quadrilateral ABCD, ∠A = 51°. For ABCD to be cyclic, ∠C must be:
  1. 129°
  2. 39°
  3. 51°
  4. 309°
8.
A transversal cuts lines l and m. Two co-interior angles are 68° and 112°. Then:
  1. l ∥ m
  2. l ⊥ m
  3. l and m meet on the side of these angles
  4. l and m meet on the other side
Section B — Short answer8 × 2 = 16 marks
9.
Write the converse of: 'If two triangles are congruent, then their areas are equal.' Is the converse true?
10.
Check whether a triangle with sides 12 cm, 16 cm, 21 cm is right-angled.
11.
Show by a counterexample that 'If a number is divisible by 6 and by 9, then it is divisible by 54' is false.
12.
In △DEF, ∠F = 22° and ∠D = 79°. Which two sides are equal?
13.
A quadrilateral has angles ∠A = 116°, ∠B = 91°, ∠C = 59° and ∠D = 94°. Is it cyclic?
14.
In △ABC, D is the midpoint of AB, and the line through D parallel to BC meets AC at E. If AC = 22 cm and BC = 32 cm, find AE and DE.
15.
A transversal cuts lines l and m. Two alternate interior angles are (5x − 7)° and (2x + 65)°. For which value of x is l ∥ m?
16.
Can a triangle have angles 48°, 36° and 96°?
Section C — Word problems4 × 4 = 16 marks
17.
Rahul marks 40 cm along one wall and 42 cm along the other from a corner. The distance between the marks is 59 cm. Is the corner a right angle? If not, is it more or less than 90°?
18.
Vikram claims: 'If the product of two whole numbers is a multiple of 8, then one of the numbers is a multiple of 8.' Is this true? If false, give a counterexample.
19.
A flowerbed ABCD has ∠A = 105°, ∠B = 109° and ∠C = 69°. Find ∠D. Can a circular fence pass through all four corners?
20.
In a triangular park ABC, a straight path starts at the midpoint D of side AB and runs parallel to BC until it meets AC at E. If BC = 360 m and AC = 400 m, how long is the path and how far is E from A?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 9 · Mathematics

Answer key

Propositions and their Converses · AW-9M-PRP-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) either true or false, but not both—
2(a) If two angles of a triangle are equal, then the sides opposite them are equal.swap the hypothesis and the conclusion
3(d) right-angled802 + 842 = 13456 = 1162
4(c) 6 cmsides opposite equal angles are equal
5(a) 5050 = 5 × 10, but 50 ÷ 15 leaves remainder 5
6(d) equal corresponding angles made by a transversalthe converse of the corresponding angles property
7(a) 129°opposite angles of a cyclic quadrilateral add up to 180°: 180° − 51°
8(a) l ∥ m68° + 112° = 180°
9If two triangles have equal areas, then they are congruent. False.False: right triangles with legs 2 and 6, and 3 and 4, both have area 6
10No, it is obtuse-angled122 + 162 = 400 < 212 = 441
11180 is divisible by 6 and 9, but not by 54180 = 6 × 30 = 9 × 20, but 180 ÷ 54 leaves remainder 18; it works because 6 and 9 share the factor 3
12DF = EF∠E = 180° − 22° − 79° = 79°, so ∠D = ∠E and the sides opposite them are equal
13No∠A + ∠C = 175°, not 180°
14AE = 11 cm, DE = 16 cmE is the midpoint of AC (converse of the mid-point theorem), so AE = 22 ÷ 2; then DE = ½ BC = 32 ÷ 2
15x = 24l ∥ m when the alternate angles are equal: 5x − 7 = 2x + 65 gives x = 24, and each angle is 113°
16Yes48° + 36° + 96° = 180°
17No, it is more than 90°402 + 422 = 3364 < 592 = 3481
18False: 4 × 4 = 1616 = 8 × 2, but neither 4 nor 4 is a multiple of 8
19∠D = 77°; no∠D = 360° − 105° − 109° − 69° = 77°; ∠A + ∠C = 174°, not 180°
20DE = 180 m, AE = 200 mconverse of the mid-point theorem: E is the midpoint of AC, and DE = ½ BC