# Free The Triangle and Its Properties 02 Practice Test - 7th grade

### Question 1

A

#### SOLUTION

Solution :A

medianis line joining a vertex of a triangle to the mid-point of the opposite side.

### Question 2

It is given that ∠OBC is 90∘.

Then, B must be the midpoint of CE.

True

False

#### SOLUTION

Solution :B

A

medianconnects a vertex of a triangle to the mid point of the opposite side.

Analtitudeis a perpendicular on one of the sides from the opposite vertex.

As OB is the altitude, B may or may not be the midpoint of CE.

### Question 3

A triangle with all the three angles less than 60 degree is possible.

True

False

#### SOLUTION

Solution :B

A triangle with all the three angles less than 60∘ is not possible, as the sum of all the angles of a triangle is 180∘.

### Question 4

The sum of all the exterior angles of a triangle is

#### SOLUTION

Solution :Let the exterior angles of the triangle be x, y and z respectively.

Then by exterior angle property, interior angles of the triangle will be (180−x)∘, (180−y)∘, (180−z)∘Using angle sum property of a triangle,

(180 - x) + (180 - y) + (180 - z) = 180

540 - (x + y + z) = 180

Therefore, x + y + z = 360∘

### Question 5

A triangle with sides 2cm, 3cm and 5cm is possible.

True

False

#### SOLUTION

Solution :B

Sum of lengths of any two sides of a triangle should always be greater than the third side.

Here, 2 + 3 = 5

Therefore, this triangle is not possible.

### Question 6

Consider the figure:

If ∠A = 50∘, ∠B = 70∘ and x = 2y, then x+y is equal to (in degrees)

#### SOLUTION

Solution :By Exterior angle property of triangles,

x + y = ∠A + ∠B

= 50∘^{ }+ 70∘

= 120∘

### Question 7

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

True

False

#### SOLUTION

Solution :A

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

### Question 8

Consider the figure:

Find the value of x + y + ∠ACB.

#### SOLUTION

Solution :

x + y + ∠ACB = 180∘ (Angles on a straight line)

### Question 9

The square of the hypotenuse is equal to the sum of the squares of the other two sides. This relation holds for all types of triangles.

True

False

#### SOLUTION

Solution :B

The square of the hypotenuse is equal to the sum of the squares of the other two sides. This relation holds only in right-angled triangles.

### Question 10

Which of the following triangles are isosceles as well as obtuse-angled triangles?

Fig 1 and Fig 3 only

Fig 2 and Fig 3 only

Fig 1, Fig 2 and Fig 4 only

Fig 1, Fig 2 and Fig 3 only

#### SOLUTION

Solution :A

An obtuse angled triangle is the triangle in which one of the angles is greater than 90∘.

An isosceles triangle is the triangle in which two sides are equal.

1. Fig 1:

ΔPQR is isosceles [∵PQ=PR]

⇒∠Q=∠R

[∵ angles opposite to equal sides of a triangle are equal]

∠P+∠Q+∠R =180∘

[angle sum property of a triangle]

∠P+25∘ +25∘ =180∘

⇒∠P=180∘ −50∘=130∘

ΔPQR is an obtuse angled triangle as one of the angles measures 130°.

2. Fig 2:

ΔABC is isosceles [∵AB=AC]

Similarly as above, we can find the angles of this triangle.

∠A=35∘,∠B=∠C=72.5∘

Since all angles are less than 90∘, ΔABC is an acute angled triangle.

3. Fig 3:

ΔXYZ is an isosceles as well as an obtuse angled triangle as angle Y measures 110°.

4. Fig 4:

ΔMNO is an isosceles as well as a right angled triangle.

Hence, only Fig 1 and Fig 3 are isosceles as well as obtuse angled triangles.