Alternate Segment Theorem

Proof of the alternate segment theorem in circle theorems about me my name is jonathan robinson and i passionate about teaching mathematics.

Alternate segment theorem. Calculate the missing angles x y and z. For easily spotting this property of a circle look out for a triangle with one of its. Ensuring they are using the correct vocabulary here is essential. The alternate segment theorem also known as the tangent chord theorem states that in any circle the angle between a chord and a tangent through one of the end points of the chord is equal to the angle in the alternate segment.

In the above diagram the angles of the same color are equal to each other. As an extension task you could ask the students to try and prove this result. The alternate segment theorem higher. Use this activity as a homework where the students must come up with a conjecture regarding the alternate segment theorem.

The following theorem is a very important result on alternate angles. This circle theorem deals with a tangent and a chord meeting at a point on a circle forming an angle between them. The angle between a tangent. In the above diagram the alternate segment theorem tells us that angle cea and angle cde are equal.

For any circle the angle between a tangent and a chord through the point of contact of the tangent is equal to the alternate segment. Consider the following figure. The chord divideds the circle into two segments. The segment that does not contain the angle between the tangent and the chord is the.

I am currently h. Try to prove this on your own before proceeding further. The alternate segment theorem states that an angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. Alternate angle segment theorem.

This theorem is called the alternate segment theorem. Is equal to the angle in the alternate segment. The proof is straightforward. More about the alternate segment theorem.