NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.4 – Part 3

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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

Triangle of PQR and PS is Bisects

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:

Triangle of ABC

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)

(Side opposite to the larger angle is larger.)