what do u mean by 'angles in the same segment'.My teacher explained a sum using this property.But I couldn't understand.PLs explain me with suitable diagram.
http://www.mathsteacher.com.au/year10/ch06_geometry/09_angles_same_segment/segment.htm
When we talk about "angles in the same segment," we are referring to a concept in geometry that applies specifically to circles. To explain this concept, let's start with a diagram.
Imagine a circle with its center labeled as O. Now, draw a chord within the circle. A chord is simply a line segment that connects two points on the circumference of the circle.
Choose any point on the circumference of the circle and label it as A. Now draw two more lines from point A to the two endpoints of the chord. These lines are called radii (plural for radius) since they connect the center of the circle to a point on the circle.
Now, we have two angles within the circle formed by these radii: ∠OAB and ∠OAC.
Angels ∠OAB and ∠OAC are said to be "angles in the same segment" because they are both connected to the same arc, which is the arc of the circle between points B and C.
The key property of angles in the same segment is that they are equal. In other words, ∠OAB = ∠OAC.
This property holds true for any chord in the circle and any point A on the circumference. So, if you have different angles within the same segment, they will always be equal.
Understanding this concept is helpful in solving various geometry problems involving circles.