Worksheet Solutions: Geometry | Mental Mathematics for Class 8 PDF Download

Q1: Which of the following statements is true about an isosceles triangle?
(a) It has three unequal sides.
(b) It has three acute angles.
(c) It has exactly two equal sides.
(d) It has no equal angles.
Ans: (c)
An isosceles triangle has two sides of equal length, and its angles opposite those sides are also equal.

Q2: In a right-angled triangle, if one acute angle is 45 degrees, what is the measure of the other acute angle?
(a) 30 degrees
(b) 45 degrees
(c) 60 degrees
(d) 90 degrees
Ans: (c)
In a right-angled triangle, the sum of the measures of the two acute angles is always 90 degrees. Therefore, the other acute angle is 90 - 45 = 45 degrees.

Q3: What is the sum of the angles of a triangle?

(a) 90 degrees
(b) 180 degrees
(c) 270 degrees
(d) 360 degrees
Ans: (b)
The sum of the angles of a triangle is always 180 degrees.

Q4: In a parallelogram, opposite sides are:
(a) Parallel
(b) Perpendicular
(c) Congruent
(d) Equal
Ans: (a)
In a parallelogram, opposite sides are parallel and equal.

Q5: If two angles of a triangle are 45 degrees and 60 degrees, what is the measure of the third angle?
(a) 45 degrees
(b) 75 degrees
(c) 90 degrees
(d) 120 degrees
Ans: (b)
The sum of the angles of a triangle is always 180 degrees. Therefore, the measure of the third angle is 180 - 45 - 60 = 75 degrees.

Q6: Fill in the Blanks
(i) The sum of the angles of a quadrilateral is __________ degrees.
Ans: 360 degrees

(ii) The measure of each interior angle of a regular hexagon is __________ degrees.
Ans: 120 degrees

(iii) The sum of the angles of a straight line is __________ degrees.
Ans: 180 degrees

(iv) A triangle with all sides of different lengths is called a(n) __________ triangle.
Ans: Scalene

(v) The opposite angles of a parallelogram are __________ in measure.
Ans: Equal

Q7: True or False
(i) An equilateral triangle is also an isosceles triangle. (True/False)
Ans: True

(ii) The area of a rectangle is equal to the product of its length and width. (True/False)
Ans: True

(iii) The diagonals of a square are perpendicular to each other. (True/False)
Ans: True

(iv) An obtuse-angled triangle can also be an isosceles triangle. (True/False)
Ans: True

(v) All right-angled triangles are similar. (True/False)
Ans: False

Q8: Mixed Difficulty
(i) If the base angles of a triangle are equal, what type of triangle is it? Explain your answer.
Ans: Isosceles Triangle

(ii) A rectangle has a perimeter of 32 units. If its length is 10 units, find its width.
Ans: 6 units

(iii) In a triangle, one angle measures 75 degrees, and the other two angles are equal. Find the measure of each of the equal angles.
Ans: 52.5 degrees

(iv) Find the area of a trapezium with a height of 8 cm and bases of length 12 cm and 16 cm.
Ans: 120 square cm

(v) ABCD is a parallelogram. If the measure of angle ABC is 120 degrees, find the measure of angle ADC.
Ans: 60 degrees