Question

Theorem 10.9 of class 9 ncert​

Answer 1

Answer:

Angles in the same segment of a circle are equal.

Answer 2

Class 9 NCERT Theorem 10.9 is as follows:

'Angles in the same segment of a circle are equal.'

Explanation:

Given: A circle with center at O. Points P & Q on this circle subtends angles ∠PAQ and ∠PBQ at points A and B respectively.

To Prove: ㄥPAQ = ㄥPBQ

Proof: Chord PQ subtends ㄥPOQ at the center

From Theorem 10.8: Angles subtended by an arc at the center is double the angle subtended by it at any other point on circle

∴ㄥPOQ = 2ㄥPAQ …(1)

∴ ㄥPOQ = 2ㄥPBQ …(2)

From (1) & (2)

2ㄥPBQ = 2ㄥPAQ

ㄥPBQ = ㄥPAQ

Hence, Proved.