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Theorem - 2 Angles in the same segment of a circle are equal.

Given : - A circle with centre O and two angles and in the same segment.

To Prove : -

Construction : OA and OB are joined.

Statement	Reason
1. In both the figures	1. Angle at the centre = 2 angle at circumference
2. Similarly	2. Reason (1)
3.	3. Statement (1) and (2)

Theorem – 3 The angle in a semi circle is a right angle.

Given : - is a straight angle is a angle subtended by the arc APB at any point C on the semi-circle ACB.

TO Prove :

Proof :

Statements	Reason
1.	1. Angle at the centre = 2 angle at circumference
2.	2. is a straight angle
3.	3. Statement (1) & (2)