# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.4 – Part 3 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Interior Angle and Exterior Angle

Interior Angle: interior angle (or internal angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex.

Exterior Angle: exterior angle (or external angle) is an angle formed by one side of a simple polygon and a line extended an adjacent side

Q-5 In the figure and PS bisects . Prove that

Solution:

Given, and PS bisects

- To prove,

- Proof,

… equation (1) ( as angle opposite to larger side is larger.) … equation (2) (PS bisects )

… equation (3) (exterior angle of a triangle equals to the sum of opposite interior angles) … . equation (4) (exterior angle of a triangle equals to the sum of opposite interior angles)

- Adding (1) and (2)
[from (1) , (2) , (3) and (4) ]

Q-6 Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

Solution:

- Let
*l*is a line segment and B is a point lying . We drew a line AB perpendicular to*l*. Let C be any other point on*l*. - To prove,

- Proof, In ,
- Now,
( must be acute angle. (Angle sum property of a triangle)

or

(Side opposite to the larger angle is larger.)