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

A __ connects a vertex of a triangle to the mid-point of the opposite side.

#### SOLUTION

Solution :

A median is line joining a vertex of a triangle to the mid-point of the opposite side. It is given that OBC is 90.
Then, B must be the midpoint of CE.

A.

True

B.

False

#### SOLUTION

Solution : B

A median connects a vertex of a triangle to the mid point of the opposite side.
An altitude is 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.

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

A.

True

B.

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​.

The sum of all the exterior angles of a triangle is ___  (in degrees)​.

#### 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 (180x)​, (180y)​​, (180z)​​

Using angle sum property of a triangle,

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

540 - (x + y + z) = 180

Therefore, x + y + z = 360

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

A.

True

B.

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.

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

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

A.

True

B.

False

#### SOLUTION

Solution : A

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

Consider the figure: Find the value of x + y + ACB.

___

#### SOLUTION

Solution :

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

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.

A.

True

B.

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.

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

Fig 1 and Fig 3 only

B.

Fig 2 and Fig 3 only

C.

Fig 1, Fig 2 and Fig 4 only

D.

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.