NCERT Class 9, Ch.7 - Triangles: Brief synopsis

Triangle is a closed shape with three sides.

Table of Contents

Triangles can be classified on the basis of sides and angels.

1. By side
2. By angles

1. Types of triangles by Side

(a) Equilateral Side: all sides are equal
(b) Isosceles triangles
(c) Scalene triangles

(a) Equilateral Side: all sides are equal

(b) Isosceles triangles

(ii) Types of triangles by angles.

(i) Acute angled triangle : All angles less than 90⁰
(ii) Right angled triangles
(iii) Obtuse angled triangle

(i) Acute angled triangle: All angles less than 90⁰

(ii) Right angled triangles

(iii) Obtuse angled triangle

Congruence of triangles

Congruence: if two figures or objects are of the same shape and of the same size. They are called as ‘Congruent’. symbolically, we use ‘≅’ for congruence.

- Two circles of the same radii are congruent-
- Two squares of the same sides are congruent.

Rules for congruence of triangles:

(i) SAS = Side Angle Side
(ii) SSS = Side Side Side
(iii) ASA = Angle Side Angle
(iv) AAs = Angle Angle Side
(v) RHS = Right angle Hypotenuse Side

(i) SAS (Side Angle Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent.

(ii) SSS (Side Side Side) : If three sides of one triangle are equal to three of the other triangles, then the two triangles are congruent.

(iii) ASA (Angle Side Angle: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent.

(iv) AAS (Angle Angle Side: If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.

(v) RHS (Right angle Hypotenuse Side): If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent .