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CBSE Class 10  >  Class 10 Test  >  Online MCQ Tests  >  Assertion & Reason Test: Triangles - 2 - Class 10 MCQ

Triangles - 2 - Free Assertion & Reason Questions with Solutions


MCQ Practice Test & Solutions: Assertion & Reason Test: Triangles - 2 (10 Questions)

You can prepare effectively for Class 10 Online MCQ Tests for Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Assertion & Reason Test: Triangles - 2". These 10 questions have been designed by the experts with the latest curriculum of Class 10 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 20 minutes
  • - Number of Questions: 10

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Assertion & Reason Test: Triangles - 2 - Question 1
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : Two similar triangle are always congruent.

Reason : If the areas of two similar triangles are equal then the triangles are congruent.

Detailed Solution: Question 1

Two similar triangles are not congruent generally.

So, A is incorrect but R is correct.

Assertion & Reason Test: Triangles - 2 - Question 2
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : ABC is an isosceles triangle right angled at C then AB2 = 2AC2.

Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Detailed Solution: Question 2

We know that If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This is converse of Pythagoras theorem.

So, Reason is correct By

Pythagoras theorem, we have AB2 = AC2 + BC2

= AC2 + AC2 [∵ AC = BC Given]

⇒ AB2 = 2AC2

So, Assertion is also correct.

But reason (R) is not the correct explanation of assertion (A).

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Assertion & Reason Test: Triangles - 2 - Question 3
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : ΔABC is an isosceles triangle right angled of C , then AB2 = 2AC2.

Reason : In right ΔABC , right angled at B, AC2 =AB2 +BC2.

Detailed Solution: Question 3

In an isosceles ΔABC , right angled at C is

AB2 = AC2 + BC2

AB2 = AC2 + AC2

AB2 = 2AC2 (AC = BC)

So, both A and R are correct and R explains A.

Assertion & Reason Test: Triangles - 2 - Question 4
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : ABC is an isosceles triangle with AC = BC. If AB2 = 2 AC2, then ΔABC is a right triangle.

Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Detailed Solution: Question 4

We know that If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. This is converse of Pythagoras theorem.

So, Reason is correct

AB2 = 2AC2 = AC2 + AC2

= BC2 + AC2 [∵ AC = BC Given]

⇒ AB2 = BC2 + AC2

By converse of Pythagoras theorem, ΔABC is a right angled triangle.

So, Assertion is also correct.

Assertion & Reason Test: Triangles - 2 - Question 5
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2 then, AB : DE = 6 :7

Reason : If ΔABC ~ ΔDEF , then ar(ΔABC)/ar(ΔDEF) = AB2/DE2 = BC2/EF2 = AC2/DF2

Detailed Solution: Question 5

ar(ΔABC)/ar(ΔDEF) = AB2/DE2

36/49 = AB2/DE2

AB/DE = 6/7

AB:DE = 6:7

So, both A and R are correct and R explain A.

Assertion & Reason Test: Triangles - 2 - Question 6
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.

Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Detailed Solution: Question 6

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

So, Reason is correct

Now, AB2 + BC2 = 242 + 102

= 576 + 49 = 625

= AC2

⇒ AB2 + BC2 = AC2

By converse of Pythagoras theorem, ∆ABC is a right angled triangle.

So, Assertion is also correct.

But reason (R) is not the correct explanation of assertion (A).

Assertion & Reason Test: Triangles - 2 - Question 7
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : In ∆ABC , DE|| BC such that AD = (7x - 4)cm, AE = (5 - 2)cm, DB = (3 + 4) cm and EC = 3 cm than x equal to 5.

Reason : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distant point, than the other two sides are divided in the same ratio.

Detailed Solution: Question 7

We have,

AD/DB = AE/EC

21x2 - 12x = 15x2 + 20x - 6x - 8x

6x2 - 26x + 8 = 0

3x2 - 13x + 4 = 0

3x2 - 12x - x + 4 = 0

3x(x - 4) - 1(x - 4) = 0

(x - 4) (3x - 1) = 0

So, A is incorrect but R is correct.

Assertion & Reason Test: Triangles - 2 - Question 8
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : If a line intersects sides AB and AC of a Δ ABC at D and E respectively and is parallel to BC, then AD/AB = AE/AC

Reason : If a line is parallel to one side of a triangle then it divides the other two sides in the same ratio.

Detailed Solution: Question 8

We know that If a line is parallel to one side of a triangle then it divides the other two sides in the same ratio. This is Basic Proportionality theorem.

So, Reason is correct.

By Basic Proportionality theorem, we have AD/DB = AE/EC

So, Assertion is correct

Assertion & Reason Test: Triangles - 2 - Question 9
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AE

Reason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.

Detailed Solution: Question 9

Reason is true : [This is Thale’s Theorem]

For Assertion Since, DE || BC by Thale’s Theorem

Assertion (a) is true

Since, reason gives Assertion.

Assertion & Reason Test: Triangles - 2 - Question 10
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Direction: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm2 and ar(ΔDEF) = 49cm2. Then, the ratio of their corresponding sides is 6 : 7

Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Detailed Solution: Question 10

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

So, Reason is correct

So, Assertion is correct.

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About this Class 10 Practice Test

This test contains 10 MCQs on Assertion & Reason Test: Triangles - 2 with detailed solutions for each question. It is part of the Online MCQ Tests for Class 10 course on EduRev, designed to align with the current Class 10 syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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