Free The Triangle and Its Properties 03 Practice Test - 7th grade 

Question 1

A triangle can have all the three angles greater than 60∘.

A.

True

B.

False

SOLUTION

Solution : B

A triangle can't have all the three angles greater than 60∘,​ because the sum of all the three angles of a triangle is 180∘.

Question 2

If the angles of a triangle are x∘, 2x∘​ and 3x∘, then the value of x is __ (in degrees).

SOLUTION

Solution :

We know that sum of the three angles of a triangle = 180∘​

Therefore, x+2x+3x=180∘​

or,6x=180∘,
x=1806=30∘

Question 3

If AM is a median of triangle ABC, then which of the following relation will always hold good?

A.

AB + BC + CA = 2AM

B.

AB + BC + CA >​ 2AM

C.

AB + BC + CA <​ 2AM

D.

AB + BC + CA = AM

SOLUTION

Solution : B


Sum of lengths of any two sides of a triangle is always greater than the third side.
Hence,
                  AB + BM > AM
                  AC + CM > AM
Thus, AB + BC + CA > 2AM

Question 4

If a △QPR is right angled at P, then which is the longest side of the triangle?

A.

PQ

B.

QR

C.

PR

D.

Can't be determined.

SOLUTION

Solution : B

The side opposite to the greatest angle in a triangle is the longest.
Here the biggest angle is the right angle, hence QR is the longest side of the triangle.

 

Question 5

Consider the figure:

If ∠A = 70∘​, ∠ACD = 120∘​, then the value of ∠B (in degrees) is
___

SOLUTION

Solution :

By Exterior Angle Property,
∠ACD  = ∠A​ + ∠B
∠B = ∠ACD - ∠A​
       = 120∘​ - 70∘
∠B = 50∘​

Question 6

The lengths of two sides of a triangle are 13cm and 16cm. The third side should lie between 'a' cm and 'b' cm for the triangle to be formed. Find the value of a + b?


___

SOLUTION

Solution :

The third side of a triangle must be greater than the difference between the other two sides.

That is, third side > (16 - 13) which is 3.

Also, Sum of lengths of any two sides of a triangle is always greater than the third side.

That is, third side < (16+13) which is 29.

Hence, a + b = 3 + 29 = 32.

Question 7

Consider the figure:

If ∠B = 50∘, ∠ACD = 120∘, then the value of ∠A (in degrees) is .

SOLUTION

Solution :

By Exterior Angle property,
∠ACD = ∠A + ∠B
∴ ∠A =  ∠ACD - ∠B
            = 120∘​ -  50∘​
            = 70∘​

Question 8

Pythagorean triplets are a set of three numbers in which the following relation holds true:

The sum of the squares of any two numbers is equal to the square of the third number.

A.

True

B.

False

SOLUTION

Solution : B

In a group of 3 numbers, if the square of the largest number is equal to the sum of the squares of the other two numbers, then, they form a Pythagorean triplet. So, the given statement is false.

Question 9

5cm, 12cm can be two sides of a right-angled triangle.

A.

True

B.

False

SOLUTION

Solution : A

Sides of lengths 5cm, 12cm and 13cm form sides of a right angled triangle.

Question 10

Consider a right angled triangle ABC, right angled at B. Length of AC = 5 cm. ∠A = 37∘​. The sides of triangles are integers. Then, find the sum of the magnitudes of AB, BC  and ∠C.

Magnitude is defined as the absolute value. Example: If ∠A is 60 degree then, its magnitude is 60; and if length AB = 45 cm, then magnitude of AB = 45.

___

SOLUTION

Solution :

Using angle sum property of a triangle,

∠C = 53∘ 

Since the sides are integers, and the triangle is right angled; the sides are 3 and 4 centimetres respectively.

Thus, magnitude of (AB +BC +∠C) = 3 + 4 + 53 = 60

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