The Triangle And Its Properties(7th Grade > Mathematics ) Questions and answers for exam Preparation

7th Grade > Mathematics

THE TRIANGLE AND ITS PROPERTIES MCQs

Total Questions : 111 | Page 2 of 12 pages

Question 11. Find the value of the unknown. [2 MARKS]
(a)

Find The Value Of The Unknown. [2 MARKS](a) (b)

(b)

Discuss Question

:
Each part: 1 Mark each
(a)

50^{\circ} + x = 115^{\circ}

(Exterior angle of a triangle is equal to the sum of its interior opposite angles)

x = 115^{\circ} - 50^{\circ}

x = 65^{\circ}

(b)

30^{\circ} + x = 80^{\circ}

(Exterior angle of a triangle is equal to the sum of its interior opposite angles)

x = 80^{\circ} - 30^{\circ}

x = 50^{\circ}

Question 12. Median and altitude of an isosceles triangle are one and the same.

True
False
60∘
120∘

Discuss Question

Answer: Option A. -> True
:
A
In an isosceles triangle, both median and altitude are same.

Question 13. A triangle with two right angles is possible.

True
False
60∘
120∘

Discuss Question

Answer: Option B. -> False
:
B
A triangle with two right angles is not possible, as the sum of all the three angles of a triangle is

180^{\circ}

Question 14. In the given figure, if

∠ C A D = 150^{\circ}

and

∠ A B C = 60^{\circ},

then reflex

∠ A C B =

___

In The Given Figure, If ∠CAD=150∘ And ∠ABC=60∘, Then...

1 right angle
2 right angles
3 right angles
4 right angles

Discuss Question

Answer: Option C. -> 3 right angles
:
C

∠ A C B + ∠ A B C = ∠ D A C

[Exterior angle property]

∠ A C B + 60^{\circ} = 150^{\circ} ∠ A C B = 90^{\circ} ∴ Reflex ∠ A C B = 360^{\circ} - 90^{\circ} = 270^{\circ} = 3 \times 90^{\circ} = 3 right angles

Question 15. Sum of lengths of any two sides of a triangle is always equal to the third side.

True
False
60∘
120∘

Discuss Question

Answer: Option B. -> False
:
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 16. A triangle with two obtuse angles is possible.

True
False
60∘
120∘

Discuss Question

Answer: Option B. -> False
:
B
The sum of all the three angles of a triangle is

180^{\circ}

.
We know that obtuse angle is an angle which is greater than

90^{\circ}

and lessthan

180^{\circ}

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^{\circ}

.
Since the sum of 2 angles of the triangle is more than

180^{\circ}

, the sum of three angles will be more than

180^{\circ}

for sure.
This is not possible as the sum of 3 angles of a triangle is fixed i.e.

180^{\circ}

and cannot exceed this limit.
Thus, a triangle cannot have 2 obtuse angles.

Question 17. 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
PR
Can't be determined.

Discuss Question

Answer: Option B. -> False
:
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 18. 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?
___

Discuss Question

:
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 19. Consider a right angled triangle ABC, right angled at B. Length of AC = 5 cm.

∠

A =

37^{\circ}

. 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.
___

Discuss Question

:
Using angle sum property of a triangle,

∠

C =

53^{\circ}

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

Question 20. If the angles of a triangle are