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Triangles Practice

Solve chapter-level practice questions for Triangles with reveal-only solutions and quick revision support.

Practice Set 1 — Congruence Criteria

Applying SAS, ASA, AAS, SSS, RHS and using CPCT.

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Q1.
State the five congruence criteria for triangles.
Q2.
Is AAA a valid congruence criterion? Why or why not?
Q3.
In △ABC and △PQR, ∠B = ∠Q = 90°, hypotenuse AC = hypotenuse PR, and BC = QR. Are the triangles congruent? By which rule?
Q4.
In △ABC, AB = AC and AD is the bisector of ∠A meeting BC at D. Prove that BD = DC.
Q5.
Two line segments AB and CD bisect each other at O. Show that AC = BD.
Q6.
In △ABC, ∠A = ∠B. In △DEF, ∠D = ∠E, DE = AB and ∠A = ∠D. Are the triangles congruent?

Practice Set 2 — Isosceles Triangles and Inequalities

Base angles, converse, triangle inequality, angle–side relations.

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Q1.
In an isosceles triangle the vertex angle is 40°. Find the base angles.
Q2.
If two angles of a triangle are 55° each, what type of triangle is it and why?
Q3.
In △ABC, ∠A = 80° and ∠B = 40°. Which is the longest side?
Q4.
Can a triangle have sides 7 cm, 24 cm, and 25 cm? Is it right-angled?
Q5.
The lengths of two sides of a triangle are 5 cm and 9 cm. Between what values must the third side lie?
Q6.
In △PQR, PQ > PR. What can you say about ∠R and ∠Q?

Quick Q&A Before You Revise

What is the difference between congruent and similar triangles?

Congruent triangles have the same shape and the same size (all corresponding sides and angles equal). Similar triangles have the same shape but possibly different sizes (corresponding angles equal, corresponding sides in proportion). Class 9 focuses on congruence.

Why is 'SSA' not a congruence rule?

Two sides and a non-included angle do not fix a triangle uniquely — two different triangles can be drawn with the same SSA data (the 'ambiguous case'). Only SAS, ASA, AAS, SSS, and RHS guarantee congruence.

What does CPCT mean and when is it used?

CPCT stands for 'Corresponding Parts of Congruent Triangles (are equal)'. Once two triangles are proved congruent by a criterion, CPCT lets you conclude that any pair of corresponding sides or angles is equal.

How do you quickly check whether three given lengths can form a triangle?

Add the two shorter lengths. If their sum is greater than the longest length, a triangle is possible; if it is equal or smaller, it is not.

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