Explore Exams
Login Signup
Sign in Open App
CBSE Class 10  >  Class 10 Test  >  Mathematics (Maths)   >  Assertion & Reason Test: Triangles - Class 10 MCQ

Triangles - Free Assertion & Reason Questions with Solutions Class 10 Maths


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

You can prepare effectively for Class 10 Mathematics (Maths) Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Assertion & Reason Test: Triangles". 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

Sign up on EduRev for free to attempt this test and track your preparation progress.

Assertion & Reason Test: Triangles - Question 1
Save

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

Assertion (A): In an equilateral triangle of side 3√3 cm, then the length of the altitude is 4.5 cm.

Reason (R): If a ladder 10 cm long reaches a window 8 cm above the ground, then the distance of the foot of the ladder from the base of the wall is 6 cm.

Detailed Solution: Question 1

In case of assertion

ΔABD, ∠D = 90°

or

or

or, h2 = 81/4

∴ h = 9/2 = 4.5 m

∴ Assertion is correct.

In case of reason: Let BC be the height of the window above the ground and AC be a ladder.

Here, BC = 8 cm and AC = 10 cm

∴ In right angled triangle ABC, AC2 = AB2 + BC2

(By using Pythagoras Theorem)

⇒ (10)2 = AB2 + (8)2

⇒ AB2 = 100 – 64

= 36

⇒ AB = 6 cm.

∴ Reason is correct.

Hence, both assertion and reason are correct but reason is not the correct explanation for assertion.

Assertion & Reason Test: Triangles - Question 2
Save

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 ΔABC , AB = 24 cm , BC = 10 cm and AC = 26 cm , then ΔABC is a right angle triangle.

Reason : If in two triangles, their corresponding angles are equal, then the triangles are similar.

Detailed Solution: Question 2

We have, AB2 + BC2 = (24)2 + (10)2

= 576 + 100 = 676 = 2

AB2 + BC2 = AC2

ABC is a right angled triangle.

Also, two triangle are similar if their corresponding angles are equal.

So, both A and R are correct but R does not explain A.

Clear all your doubts with EduRev
Assertion & Reason Test: Triangles - Question 3
Save

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

Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cm

Reason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Detailed Solution: Question 3

We know that In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This is Pythagoras theorem. So, Reason is correct

Let the side of square be x cm.

In ∆ABD, by Pythagoras theorem, we have BD2 = AB2 + AD2

⇒ 162 = x2 + x2

⇒ 2x2 = 256 ⇒ x2 = 128 ⇒ x = 8√2 cm

So, Assertion is also correct.

Assertion & Reason Test: Triangles - Question 4
Save

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

Assertion (A): Corresponding sides of two similar triangles are in the ratio of 2 : 3. If the area of the smaller triangle is 48 cm2, then the area of the larger triangle is 108 cm2.

Reason (R): If D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC, then CA2 = CB × CD.

Detailed Solution: Question 4

In case of assertion

Let ΔABC and ΔDEF are two similar triangles.

Given that ar ΔABC = 48 cm2. Then,

Thus, the area of larger triangle is 108 cm2.

∴ Assertion is correct.

In case of reason:

In ΔBAC and ΔADC,

∠BAC= ∠ADC [Given]

∠BCA= ∠ACD [Common angle]

By AA similarity, ΔBAC ~ ΔADC

Thus,

CA/CD = BC/CA

∴ Reason is correct.

Hence, both assertion and reason are correct but reason is not the correct explanation for assertion.

Assertion & Reason Test: Triangles - Question 5
Save

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 and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm2 , then area of ΔDEF = 100 cm2.

Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.

Detailed Solution: Question 5

Given: ΔABC ∼ ΔDEF, BC = 4 cm, EF = 5 cm, Area of ΔABC = 64 cm2.

For two similar triangles, the ratio of their areas is equal to the square of the ratio of corresponding sides:
Area of ΔABC / Area of ΔDEF = (BC / EF)2
64 / Area of ΔDEF = (4 / 5)2 = 16 / 25
Area of ΔDEF = (64 × 25) / 16 = 100 cm2

The reason given is also true because the areas of similar triangles are in the ratio of the squares of corresponding altitudes, which correctly explains the assertion.

Assertion & Reason Test: Triangles - Question 6
Save

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

Assertion : The areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.

Reason : The ratio of the areas of two similar triangles is equal to 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 not correct

So, Assertion is correct

Assertion & Reason Test: Triangles - Question 7
Save

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

Assertion (A): If D is a point on side QR of ΔPQR such that PD ⊥ QR, then ΔPQD ~ ΔRPD.

Reason (R): In the figure given below, if ∠D = ∠C then ΔADE ~ ΔACB.

Detailed Solution: Question 7

In case of assertion

In ΔPQD and ΔRPD, ∠PDQ = ∠PDR= 90°.

There is no other information to be similar.

Thus, it is not it will be correct to say that ΔPQD ~ ΔRPD.

∴ Assertion is incorrect.

In case of reason:

In ΔADE and ΔACB, we have

∠ADE= ∠ACB [Given]

∠DAE= ∠CAB [Common angle]

By AA similarity, we get ΔADE ~ ΔACB.

∴ Reason is correct

Hence, assertion is incorrect but reason is correct

Assertion & Reason Test: Triangles - Question 8
Save

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, right triangle, right angled at C . Then AB2 = 3AC2

Reason : In an isosceles triangle ABC if AC = BC and AB2 = 2AC2 , then ∠C = 90°

Detailed Solution: Question 8

If Assertion is incorrect, but Reason is correct.

In right angled ΔABC ,

AB2 = AC2 + BC2(By Pythagoras Theorem)

= AC2 + AC2 [BC = AC]

= 2AC2AB2 = 2AC2

Assertion is false.

Again since, AB2 = 2AC2

= AC2 + AC2 = AC2 + BC2 (AC = BC given)

∠ = 90°

(By converse of Pythagoras Theorem)Reason is true.

Assertion & Reason Test: Triangles - Question 9
Save

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 , AB = 6√3, AC = 12 cm and BC = 6cm then ∠B = 90°.

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 9

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

Now, AB2 = (6√3)2 = 108

AC2 = 122 = 144

and BC2 = 62 = 36

∴ 2 = 2 + 2

By converse of Pythagoras theorem, ∠B = 90°

So, Assertion is also correct.

Assertion & Reason Test: Triangles - Question 10
Save

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

Assertion (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.

Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then the

ratio of their areas is 6/5.

Detailed Solution: Question 10

In case of assertion: In the given two right triangles, both have equal right angles and one of the acute angles of one triangle is equal to an acute angle of the other triangle.

Thus, by AA similarity, the given two triangles are similar.

∴ Assertion is correct.

In case of reason:

We know that the ratio of the areas of two similar triangles is the square of the ratio of the corresponding altitudes of two similar triangles.

Thus, the ratio of the areas of two similar triangles is (3/5)2 = 9/25.

118 videos|526 docs|45 tests
Join Course
Information about Assertion & Reason Test: Triangles Page
In this test you can find the Exam questions for Assertion & Reason Test: Triangles solved & explained in the simplest way possible. Besides giving Questions and answers for Assertion & Reason Test: Triangles, EduRev gives you an ample number of Online tests for practice
118 videos|526 docs|45 tests
Join Course
Download as PDF

About this Class 10 Practice Test

This test contains 10 MCQs on Assertion & Reason Test: Triangles with detailed solutions for each question. It is part of the Mathematics (Maths) 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.

Explore more Class 10 Study Resources

If you found this Assertion & Reason Test: Triangles MCQ Test helpful, you can further enhance your Class 10 preparation with in-depth courses on EduRev, for all the subjects and topics available in Mathematics (Maths) Class 10 course. The course offers:
  • Video Lectures: covering all the topics of Mathematics (Maths) Class 10
  • Notes for Revision: offering revision notes, important questions, summaries, flashcards, cheatsheets & more for Class 10 preparation
  • MCQ Test: variety of questions as per the pattern of Class 10 exam
Signup to see your scores go up
within 7 days!
Takes less than 10 seconds to signup