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

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.

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

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

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.

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

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.

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

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.

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.

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