NCERT Solutions for Class 9 Maths Chapter 7

Properties of a Triangle
1. Angle opposite to equal sides of an isosceles triangle are equal.
2. The sides opposite to equal angles of a triangle are equal.
3. If two sides of a triangle are unequal then the angle opposite to the longer side is larger.
4. In any triangle, the side opposite to the larger angle is larger.
5. The sum of any two sides of a triangle is greater than the third side.
6. The difference between any two sides of a triangle is less than its third side.
7. If the bisector of the vertical angle of a triangle bisects the base, then triangle is an isosceles triangle.
8. The sum of any two sides of a triangle is greater than twice the median drawn to the third side.

Triangle: A plane figure closed by three intersecting lines is called a triangle. Here, ‘Tri’ means THREE. A triangle has three sides, three angles and three vertices.

Draw perpendicular bisectors of AB, BC and AC, which intersects each other at G. Point G is equidistant from the three vertices of ΔABC.

Draw the bisectors of ∠A, ∠B and ∠C, which intersect each other at O. Point O is equidistant from the three sides of ΔABC i.e. OP = OQ = OR.

In ΔABD and ΔACD, ∠ADB = ∠ADC [∵ Each 90°] AB = AC [∵ Given] AD = AD [∵ Common] Hence, ΔABD ≅ ΔACD [∵RHS Congruency Rule] BD = DC [∵ CPCT] Hence, AD bisects BC

In ΔABP and ΔACP, ∠APB = ∠APC [∵ Each 90°] AB = AC [∵ Given] AP = AP [∵ Common] Hence, ΔABP ≅ ΔACP [∵RHS Congruency Rule] ∠B = ∠C [∵ CPCT]