Triangles Practice Questions
Class 9 · Mathematics · 3047 free MCQs with instant results and detailed explanations.
3047
Total
968
Easy
1475
Medium
604
Hard
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Topics in Triangles
Properties of Triangle
683
Congruence of Triangles
846
Inequalities in Triangle
664
Criteria for Congruence
854
Sample Questions from Triangles
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
If triangle ABC is congruent to triangle DEF, then which of the following is true?
A.
AB = DE
B.
AC = EF
C.
BC = FD
D.
All of the above
Show Answer & Explanation
Correct Answer: D
If two triangles are congruent, then all corresponding sides and angles are equal, making all statements true.
Q2
Easy
Which congruence criterion is represented by the statement 'two angles and the included side are equal'?
A.
ASA
B.
SAS
C.
AAS
D.
SSS
Show Answer & Explanation
Correct Answer: A
The ASA criterion (Angle-Side-Angle) states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
Q3
Easy
In triangle PQR, if PQ = 6 cm, QR = 8 cm, and PR = 10 cm, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Scalene
Show Answer & Explanation
Correct Answer: C
Using the Pythagorean theorem, if the square of the longest side equals the sum of the squares of the other two sides, it is a right triangle.
Q4
Medium
Which of the following pairs of triangles are congruent by the SSS criterion?
A.
Triangle ABC with sides 5 cm, 7 cm, 9 cm and Triangle DEF with sides 5 cm, 7 cm, 9 cm
B.
Triangle XYZ with sides 4 cm, 6 cm, 8 cm and Triangle PQR with sides 4 cm, 6 cm, 7 cm
C.
Triangle KLM with angles 60°, 70°, 50° and Triangle NOP with angles 60°, 70°, 50°
D.
Triangle GHI with sides 3 cm, 4 cm, 5 cm and Triangle JKL with sides 3 cm, 5 cm, 7 cm
Show Answer & Explanation
Correct Answer: A
The SSS criterion states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
Q5
Medium
If two triangles have two angles equal, what can be said about the triangles?
A.
They are not congruent.
B.
They are similar.
C.
They are congruent.
D.
They cannot be compared.
Show Answer & Explanation
Correct Answer: B
Triangles with two equal angles are always similar, but not necessarily congruent unless the sides between those angles are also equal.
Q6
Medium
Two triangles are congruent by the ASA criterion. If one angle of triangle A is 50° and the angle adjacent to it in triangle B is 50°, what can be said about the triangles?
A.
They have equal sides.
B.
They are similar.
C.
They cannot be compared.
D.
They are congruent.
Show Answer & Explanation
Correct Answer: D
The ASA criterion states that if two angles and the included side of one triangle are equal to the corresponding parts of another triangle, they are congruent.
Q7
Medium
Which of the following sets of triangles can be proven congruent using the RHS criterion?
A.
Right triangle with sides 6 cm, 8 cm and another with sides 8 cm, 6 cm
B.
One right triangle with hypotenuse 10 cm and one leg 6 cm, and another with hypotenuse 10 cm and one leg 7 cm
C.
Right triangle with legs 5 cm, 12 cm and another right triangle with legs 5 cm, 12 cm
D.
Two right triangles with hypotenuse 13 cm and one leg 5 cm but different other leg lengths.
Show Answer & Explanation
Correct Answer: C
The RHS (Right angle-Hypotenuse-Side) criterion states that if the hypotenuse and one leg of a right triangle are equal to those of another right triangle, the triangles are congruent.
Q8
Hard
In triangle ABC, if angle A = 45°, angle B = 55°, and side a = 10 cm, what is the length of side b using the Law of Sines?
A.
8.5 cm
B.
7.5 cm
C.
9.0 cm
D.
6.0 cm
Show Answer & Explanation
Correct Answer: A
Using the Law of Sines: a/sin(A) = b/sin(B). Plugging in values gives b = (10 * sin(55°)) / sin(45°) ≈ 8.5 cm.
Q9
Hard
Which of the following sets of conditions will guarantee that two triangles are congruent?
A.
SSS
B.
SAS
C.
ASA
D.
All of the above
Show Answer & Explanation
Correct Answer: D
All three conditions (SSS, SAS, ASA) ensure that two triangles are congruent as they define a unique triangle.
Q10
Hard
In which situation can we conclude that two triangles are not congruent?
A.
One triangle has three sides longer than the corresponding sides of another triangle.
B.
Both triangles have equal angles.
C.
One triangle has two sides equal to those in another triangle.
D.
One triangle is a right triangle while the other is not.
Show Answer & Explanation
Correct Answer: A
If one triangle has all sides longer than the corresponding sides of another, they cannot be congruent.
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Triangles — Class 9 Mathematics Practice Questions Online
This page contains 3047 practice MCQs for the chapter Triangles in Class 9 Mathematics. The questions are organized by difficulty — 968 easy, 1475 medium, 604 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.