Page 157 - Math Skill - 5

Geometry 155

Exercise 12.3

1. Fill in the blanks.
(a) The distance between the parallel lines is always __________.

(b) Two parallel lines never __________ when produced on either sides.
(c) Two intersecting lines, when make an angle of 90°, are called __________ lines.

(d) If ∠ABX = 90°, this implies AB is __________ to BX.
(e) Coplanar lines lie in the same __________.

(f) Two lines can intersect at __________ and only __________ point.

2. Find the number of pairs of perpendicular and parallel lines in the following figures:

(a) R (b) A H
P
S O B G

L Q C F
M N D E

Triangles and Their Classification

A triangle has three sides and three angles which are called the elements of a triangle. The
symbol ‘∆’ is used to denote a triangle.
We classify the triangles on the basis of the lengths of their sides and on the basis of the measures
of their angles.

On the basis of the lengths of their sides, triangles are of three types.

Scalene Triangle
A
If all the three sides of a triangle are of different lengths, then
it is called a scalene triangle. In the figure, ∆ABC is a scalene 4 cm 3 cm
triangle with AB = 4 cm, BC = 5 cm and CA = 3 cm. B 5 cm C

Thus, AB ≠ BC ≠ CA
Also, the angles of a scalene triangle are never equal, thus, ∠A ≠ ∠B ≠ ∠C.

Isosceles Triangle
P
In a triangle, if any two sides are of equal length then it is called an
isosceles triangle. In the figure, ∆PQR is an isosceles triangle because
PQ = PR = 4 cm. When we measure ∠Q and ∠R, we will find that 4 cm 4 cm
∠Q = ∠R. Thus, in an isosceles triangle, the angles corresponding to
the equal sides are always equal. Q 3.5 cm R