The lengths of the sides of a triangle are 7 cm, 8 cm, and 9 cm. The length of the altitude to the longest side is:
(a) 4√5 cm
(b) 6√5 cm
(c) (8√5)/3 cm
(d) (12√5)/3 cm

In a triangle ABC, if the exterior angle at vertex B is 110° and ∠A = 45°, what is the measure of ∠C?
(a) 55°
(b) 60°
(c) 65°
(d) 70°

The proposition that the three interior angles of any triangle sum to two right angles is an example of a:
A) Definition
B) Postulate
C) Axiom
D) Theorem

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

The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. What is the area of the triangle?
(a) 32√2 cm²
(b) 48√2 cm²
(c) 32√3 cm²
(d) 16√3 cm²

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)

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

Euclid’s first three postulates essentially state the usability of which two basic geometric tools?
A) Protractor and ruler
B) Straightedge and compass
C) Scale and protractor
D) Compass and T-square

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

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°

Two straight lines AB and CD intersect at a point O. If ∠AOC = 45°, then what is the measure of ∠BOD?
(a) 45°
(b) 55°
(c) 135°
(d) 90°

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

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

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

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