# Free The Triangle and Its Properties 01 Practice Test - 7th grade

### Question 1

Two angles of a triangle are 50∘ and 70∘. The third angle is:

50∘

70∘

60∘

120∘

#### SOLUTION

Solution :C

The sum of all the angles of a triangle is 180∘.

Therefore,

Third angle=180∘ −( 50∘ + 70∘ ) =180∘ −( 120∘ ) =60∘

### Question 2

Pythagoras' theorem holds good for right angled triangles.

True

False

#### SOLUTION

Solution :A

In a right angled triangle, square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides. This is Pythagoras' theorem.

### Question 3

**Median **and **altitude **of an isosceles triangle are one and the same.

True

False

#### SOLUTION

Solution :A

In an isosceles triangle, both

medianandaltitudeare same.

### Question 4

A triangle with two obtuse angles is possible.

True

False

#### SOLUTION

Solution :B

The sum of all the three angles of a triangle is 180∘.

We know that obtuse angle is an angle which is greater than 90∘ and less than 180∘

Hence a triangle cannot have two obtuse angles.

The sum of 2 obtuse angles will be greater than (90 + 90), i.e. greater than 180∘.

Since the sum of 2 angles of the triangle is more than 180∘, the sum of three angles will be more than 180∘ for sure.

This is not possible as the sum of 3 angles of a triangle is fixed i.e. 180∘ and cannot exceed this limit.

Thus, a triangle cannot have 2 obtuse angles.

### Question 5

Sum of lengths of any two sides of a triangle is always equal to the third side.

True

False

#### SOLUTION

Solution :B

Sum of lengths of any two sides of a triangle is always greater than the third side. Hence, the given statement is false.

### Question 6

The six elements of a triangle are its ‘a’ sides and ‘b’ angles. Find the value of a×b.

#### SOLUTION

Solution :The six elements of a triangle are 3 sides and 3 angles. Hence, 3×3=9.

### Question 7

Consider the figure:

If BC = AC and angle ACB = 60^{o}, then find the value of ∠A + ∠B + ∠x + ∠y .

#### SOLUTION

Solution :Given ∠C = 60

^{o}and BC = AC,

Therefore ∠A=∠B (base angles are equal in an isosceles triangle)

∴ by angle sum property of triangle, ∠A=∠B=60oWe know that, ∠x +∠y = ∠A +∠B (Exterior angle property)

∴ ∠A+∠B+∠x+∠y=60∘+60∘+120∘=240∘

### Question 8

Consider the figure:

If BC = AC, x = 2y, and angle ∠ACB = 60^{o}, then the value of ∠B + y (in degrees) is

#### SOLUTION

Solution :∠C = 60∘ and BC = AC,

By angle sum property of triangle, ∠A = ∠B = 60∘Also,

∠ACB+∠x+∠y=1800 [ BCD is straight line]

⟹60∘+2y+y=180∘

⟹60∘+3y=180∘

⟹3y=180∘−60∘

⟹y=40∘Hence, ∠B+y=60∘+40∘=100∘

### Question 9

A triangle with two right angles is possible.

True

False

#### SOLUTION

Solution :B

A triangle with two right angles is not possible, as the sum of all the three angles of a triangle is 180∘.

### Question 10

In the given figure, if ∠CAD=150∘ and ∠ABC=60∘, then reflex ∠ACB=

1 right angle

2 right angles

3 right angles

4 right angles

#### SOLUTION

Solution :C

∠ACB + ∠ABC= ∠DAC

[Exterior angle property]

∠ACB + 60∘=150∘ ∠ACB=90∘∴ Reflex ∠ACB =360∘−90∘ =270∘ =3×90∘ =3 right angles