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Math Olympiad Test: Triangles - 1 - Class 10 MCQ


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10 Questions MCQ Test Olympiad Preparation for Class 10 - Math Olympiad Test: Triangles - 1

Math Olympiad Test: Triangles - 1 for Class 10 2024 is part of Olympiad Preparation for Class 10 preparation. The Math Olympiad Test: Triangles - 1 questions and answers have been prepared according to the Class 10 exam syllabus.The Math Olympiad Test: Triangles - 1 MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Math Olympiad Test: Triangles - 1 below.
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Math Olympiad Test: Triangles - 1 - Question 1

In ΔABC, ∠B = 70°, ∠C = 50° then ∠BAD =?

Detailed Solution for Math Olympiad Test: Triangles - 1 - 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

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 for Math Olympiad Test: Triangles - 1 - 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

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 for Math Olympiad Test: Triangles - 1 - Question 3

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

Math Olympiad Test: Triangles - 1 - Question 4

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 for Math Olympiad Test: Triangles - 1 - Question 4

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



Math Olympiad Test: Triangles - 1 - Question 5

In a triangle ABC, ∠B = 55°, ∠C = 35° then which of the following option is true?

Detailed Solution for Math Olympiad Test: Triangles - 1 - 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

In the figure given below, what is the measures of angle ∠DAE?

Detailed Solution for Math Olympiad Test: Triangles - 1 - Question 6

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

Math Olympiad Test: Triangles - 1 - Question 7

Two isosceles triangles with equal vertical angles have their areas in the ratio 225 : 289. What is the ratio between corresponding altitudes?

Detailed Solution for Math Olympiad Test: Triangles - 1 - 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


ΔABC ~ ΔPQR such that ∠A=∠P and ∠B=∠Q
What is if BC : QR = 9 : 7?

Detailed Solution for Math Olympiad Test: Triangles - 1 - Question 8


Math Olympiad Test: Triangles - 1 - Question 9

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 for Math Olympiad Test: Triangles - 1 - Question 9

Math Olympiad Test: Triangles - 1 - Question 10

Triangle ABC is right-angled at C and AC = √3 BC. What is ∠ABC equal to ?

Detailed Solution for Math Olympiad Test: Triangles - 1 - 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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