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CBSE Class 10  >  Class 10 Test  >  Olympiad Preparation  >  Math Olympiad Test: Triangles - 1 - Class 10 MCQ

Math Olympiad Test: Triangles - 1 - Free MCQ with solutions Class 10


MCQ Practice Test & Solutions: Math Olympiad Test: Triangles - 1 (10 Questions)

You can prepare effectively for Class 10 Olympiad Preparation for Class 10 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Math Olympiad Test: Triangles - 1". 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: 10 minutes
  • - Number of Questions: 10

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Math Olympiad Test: Triangles - 1 - Question 1
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In ΔABC, ∠B = 70°, ∠C = 50° then ∠BAD =?

Detailed Solution: Question 1

In ΔABD and ΔACD

By Angle Bisector Theorem
it is given,
and ∠BAC = 180 - 70 - 50
= 180 - 120 = 60°
so, ∠BAD = 

Math Olympiad Test: Triangles - 1 - Question 2
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In ΔLMN, P and Q are the mid-points of LM and LN respectively. What is the ratio of the area of ΔLPQ, and ΔLMN?

Detailed Solution: Question 2

∵ P and Q are mid-points of ∠M and ∠N respectively
∠ PQ || MN (according to midpoint theorem) and, also,

where G and H are feets of  perpendicular dropped from L on PQ and MN respectively.

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Math Olympiad Test: Triangles - 1 - Question 3
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ABCD is a trapezium in which AB || DC and AB = 2CD. If the diagonals of the trapezium intersect each other at point O. What is the ratio of the area of ΔAOB and ΔCOD?

Detailed Solution: Question 3

∠ CAB = ∠ACD
{ Alternate opposite int erior angles}
∠BDC = ∠DBA
∴ ΔAOB ~ ΔCOD (SS similarity)

Math Olympiad Test: Triangles - 1 - Question 4
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Two poles of heights 6 m, and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m. What is the distance between their tops?

Detailed Solution: Question 4

CB = CD - BD = 11m - 6m = 5m
ED = AB = 12 m



Math Olympiad Test: Triangles - 1 - Question 5
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In a triangle ABC, ∠B = 55°, ∠C = 35° then which of the following option is true?

Detailed Solution: Question 5

∠A = 180° - (∠B + ∠C)
= 180° - (55° + 35°) = 90°
∴ ∠A is 90° or the triangle is right angled at A
∴ AB2 + AC2 = BC2 (pythagoras’ theorem)

Math Olympiad Test: Triangles - 1 - Question 6
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In the figure given below, what is the measures of angle ∠DAE?

Detailed Solution: Question 6

In ΔABC
∠BAC = 180° - (100° + 40°) = 40°
∠DAE = 180° - (50° + 40°) = 90° [linear pair]

Math Olympiad Test: Triangles - 1 - Question 7
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Two isosceles triangles with equal vertical angles have their areas in the ratio 225 : 289. What is the ratio between corresponding altitudes?

Detailed Solution: Question 7

∵ Vertical angles of isosceles Ds are identical
∴ Other two equal angles of both the Ds will be identical.
∴ By using S.S.S. similarity, we can say, that the two triangles are similar.
∴ Ratio of altitudes = 

Math Olympiad Test: Triangles - 1 - Question 8
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ΔABC ~ ΔPQR such that ∠A=∠P and ∠B=∠Q
What is if BC : QR = 9 : 7?

Detailed Solution: Question 8


Math Olympiad Test: Triangles - 1 - Question 9
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In the given figure, ∆ACB ∼ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA 

Detailed Solution: Question 9

Math Olympiad Test: Triangles - 1 - Question 10
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Triangle ABC is right-angled at C and AC = √3 BC. What is ∠ABC equal to ?

Detailed Solution: Question 10

Given:

ΔABC is right-angle at C

AC = √3BC

Formula used:

tan θ = Perpendicular/Base

tan 30° = 1/√3

Calculation:

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About this Class 10 Practice Test

This test contains 10 MCQs on Math Olympiad Test: Triangles - 1 with detailed solutions for each question. It is part of the Olympiad Preparation 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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