## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Objective Type Questions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) A triangle has at least ………… acute angles.

(ii) A triangle cannot have more than ……… right angle.

(iii) A triangle cannot have more than ………… obtuse angle.

(iv) In every triangle, the sum of (interior) angles of a triangle = ……….. right angles.

(v) In every triangle, an exterior angle + adjacent interior angle = ………… degrees.

(vi) In every triangle, an exterior angle = sum of the …….. interior opposite angles.

(vii) In a right-angled triangle, if one of the acute angles measures 25° then the measure of the other acute angle is …………

Solution:

Question 2.

State whether the following statements are true (T) or false (F):

(i) A triangle can have all three angles with a measure greater than 60°.

(ii) A triangle can have all three angles with a measure of less than 60°.

(iii) If an exterior angle of a triangle is a right angle, then each of its interior opposite angles is acute.

(iv) In a right-angled triangle, the sum of two acute angles is 90°.

(v) If all the three sides of a triangle are equal, then it is called a scalene triangle.

(vi) Every equilateral triangle is an isosceles triangle.

(vii) Every isosceles triangle must be an equilateral triangle.

(viii) Each acute angle of an isosceles right-angled triangle measures 60°.

(ix) A median of a triangle always lies inside the triangle.

(x) An altitude of a triangle always lies outside the triangle.

(xii) In a triangle, the sum of squares of two sides is equal to the square of the third side.

Solution:

**Multiple Choice Questions**

Choose the correct answer from the given four options (3 to 17):

Question 3.

A triangle formed by the sides of lengths 4.5 cm, 6 cm, and 4.5 cm is

(a) scalene

(b) isosceles

(c) equilateral

(d) none of these

Solution:

Question 4.

The number of medians in a triangle is

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

Question 5.

An exterior angle of a triangle is 125°. If one of the two interior opposite angles is 55° then the other interior opposite angle is

(a) 70°

(b) 55°

(c) 60°

(d) 80°

Solution:

Question 6.

In a ∆ABC, if ∠A = 40° and ∠B = 55° then ∠C is

(a) 75°

(b) 80°

(c) 95°

(d) 85°

Solution:

Question 7.

If the angles of a triangle are 35°, 35°, and 110°, then it is

(a) an isosceles triangle

(b) an equilateral triangle

(c) a scalene triangle

(d) right-angled triangle

Solution:

Question 8.

A triangle whose two angles measure 30° and 120° is

(a) scale

(b) isosceles

(c) equilateral

(d) none of these

Solution:

Question 9.

A triangle can have two

(a) right angles

(b) obtuse angles

(c) acute angles

(d) straight angles

Solution:

Question 10.

A triangle whose angles measure 35°, 35° and 90° is

(a) acute-angled

(b) right-angled

(c) obtuse-angled

(d) isosceles

Solution:

Question 11.

A triangle is not possible whose angles measure

(a) 40°, 65°, 75°

(b) 50°, 56°, 74°

(c) 72°, 63°, 45°

(d) 67°, 42°, 81°

Solution:

Question 12.

If in an isosceles triangle, each of the base angles is 40°, then the triangle is

(a) right-angled triangle

(b) acute-angled triangle

(c) obtuse-angled triangle

(d) isosceles right-angled triangle

Solution:

Question 13.

A triangle is not possible with sides of lengths (in cm)

(a) 6, 4, 10

(b) 5, 3, 7

(c) 7, 8, 9

(d) 3.6, 5.4, 8

Solution:

Question 14.

Which of the following can be the length of the third side of a triangle whose two sides measure 18 cm and 14 cm?

(a) 32 cm

(b) 3 cm

(c) 4 cm

(d) 5 cm

Solution:

Question 15.

In a right-angled triangle, the lengths of two leg’s are 6 cm and 8 cm. The length of the hypotenuse is

(a) 14 cm

(b) 10 cm

(c) 11 cm

(d) 12 cm

Solution:

Question 16.

If the dimensions of a rectangle are 15 m and 8 m, then the length of a diagonal is

(a) 7 m

(b) 23 m

(c) 17 m

(d) 20 m

Solution:

Question 17.

If p, q, and r are the lengths of the three sides of a triangle, then which of the following statements is correct?

(a) p + q = r

(b) p + q < r (c) p + q > r

(d) p – q > r

Solution:

**Higher Order Thinking Skills (HOTS)**

Question 1.

In ∆DEF, DM and EN are two medians. Prove that 3(DF + EF) > 2(DM + EN).

Solution:

Question 2.

In a ∆ABC, medians AD, BE and CF intersect each other at point G. Prove that 3(AB + BC + CA) > 2(AD + BE + CF).

Solution: