Geometry — Practice

Question 1

State the Basic Proportionality (Thales) theorem.

Accepted Answer

A line drawn parallel to one side of a triangle divides the other two sides in the same ratio.

Question 2

In a right triangle, base = 6 cm and height = 8 cm. Find the hypotenuse.

Accepted Answer

h² = 6² + 8² = 100 → h = 10 cm.

Question 3

The sides of two similar triangles are in ratio 2 : 3. Find the ratio of their areas.

Accepted Answer

(2 : 3)² = 4 : 9.

Question 4

From a point 13 cm from the centre of a circle of radius 5 cm, find the tangent length.

Accepted Answer

Tangent² = 13² − 5² = 144 → length = 12 cm.

Question 5

A line parallel to BC meets AB at D, AC at E with AD = 2, DB = 3, AE = 4. Find EC.

Accepted Answer

AD/DB = AE/EC → 2/3 = 4/EC → EC = 6.

Question 6

State the angle bisector theorem.

Accepted Answer

The internal bisector of an angle divides the opposite side in the ratio of the other two sides (BD/DC = AB/AC).

Practice — Geometry