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Class 9 Propositions and their Converses worksheet
CBSE Mathematics. Statements, converses and counterexamples in geometry and number theory. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
A proposition is a statement that is:
- a question
- an opinion
- always true
- either true or false, but not both
Answer
(d) 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:
- If two angles of a triangle are equal, then the sides opposite them are equal.
- If two sides of a triangle are equal, then the angles opposite them are equal.
- If a² = b², then a = b.
- If x² = 9, then x = 3.
Answer
(a) If two angles of a triangle are equal, then the sides opposite them are equal.
swap the hypothesis and the conclusion
- 3.
A triangle has sides 80 cm, 84 cm and 116 cm. It is:
- acute-angled
- not a triangle
- obtuse-angled
- right-angled
Answer
(d) right-angled
80² + 84² = 13456 = 116²
Section B · short answer
- 4.
Write the converse of: 'If two triangles are congruent, then their areas are equal.' Is the converse true?
Answer
If 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
- 5.
Check whether a triangle with sides 12 cm, 16 cm, 21 cm is right-angled.
Answer
No, it is obtuse-angled
12² + 16² = 400 < 21² = 441
Section C · long answer
- 6.
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°?
Answer
No, it is more than 90°
40² + 42² = 3364 < 59² = 3481
Fresh sheets for your child
In the app, every Propositions and their Converses sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
Coming soon for Android and iPhone.