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

### Question 1

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

True

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

#### 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?

AB + BC + CA = 2AM

AB + BC + CA > 2AM

AB + BC + CA < 2AM

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?

PQ

QR

PR

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.

True

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.

True

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