# NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.4 – Part 3 (For CBSE, ICSE, IAS, NET, NRA 2022)

Glide to success with Doorsteptutor material for CBSE/Class-9 : get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-9.

Interior Angle and Exterior Angle Give Interior Angle and Exterior Angle , Interior Angle is …

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)

[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.)

Developed by: