If one angle of a triangle is equal to the sum of the other two angles, then the triangle is:
(a) An isosceles triangle
(b) An obtuse triangle
(c) An equilateral triangle
(d) A right-angled triangle

According to Euclid’s definitions, which of the following has no parts?
(a) A line
(b) A surface
(c) A point
(d) A solid

What is the area of an equilateral triangle with a side length of 4√3 cm?
(a) 12√3 cm²
(b) 16√3 cm²
(c) 9√3 cm²
(d) 24 cm²

If a transversal intersects two parallel lines, then the bisectors of any pair of corresponding angles are:
(a) Perpendicular
(b) Intersecting
(c) Parallel
(d) Coincident

A “solid” is defined by Euclid as having:
A) Length and breadth only.
B) Length only.
C) No parts.
D) Length, breadth, and depth.

A solid has:
(a) 0 dimensions
(b) 1 dimension
(c) 2 dimensions
(d) 3 dimensions

A triangle has sides of 13 cm, 14 cm, and 15 cm. What is its area?
(a) 84 cm²
(b) 90 cm²
(c) 105 cm²
(d) 78 cm²

An angle is 14° more than its supplementary angle. What is the measure of the angle?
(a) 83°
(b) 97°
(c) 104°
(d) 52°

In triangle PQR, if ∠P = 70° and ∠R = 40°, which side of the triangle is the longest?
(a) PQ
(b) QR
(c) PR
(d) Cannot be determined

An advertisement board is in the form of a triangle with sides 12 m, 22 m, and 20 m. What is the cost of painting it at the rate of ₹5 per m²?
(a) ₹480
(b) ₹500
(c) ₹491
(d) ₹520 (approx)

If line AB is parallel to line CD, what is the value of x?
(two parallel lines AB and CD cut by a transversal. The consecutive interior angles are marked as (2x + 15)° and (3x + 5)°.)
(a) 32°
(b) 36°
(c) 40°
(d) 44°

Euclid’s fifth postulate is equivalent to:
(a) The Playfair’s Axiom
(b) The Pythagorean Theorem
(c) The Angle Sum Property
(d) The axiom that two distinct points determine a unique line

The perimeter of a triangle is 60 cm. If its sides are in the ratio 1 : 3 : 2, what is the length of the longest side?
(a) 10 cm
(b) 20 cm
(c) 30 cm
(d) 40 cm

If two angles are complementary, and one angle is 20° more than the other, what are the angles?
(a) 35°, 55°
(b) 40°, 50°
(c) 25°, 65°
(d) 30°, 60°

How many lines can be drawn passing through two distinct given points?
(a) Zero
(b) One
(c) Two
(d) Infinitely many