Question

Please help me on this!

Answer 1

The Proof is given below.

Explanation:

Given:

P is the center of Circle

∠ONE ≅ ∠TEN

To Prove:

∠5 ≅ ∠6

Proof:

Exterior Angle Theorem:

Exterior Angle Property of a Triangle states that measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles.

STATEMENT REASON

1. So In ΔONE,

`\angle 5=\angle ONE+\angle 2` 1. Exterior Angle Property of a Triangle.

2. Similarly In ΔTEN,

`\angle 6=\angle TEN+\angle 1` 2. Exterior Angle Property of a Triangle.

3. But , ∠ONE ≅ ∠TEN 3. Given

4. And P is the center of circle So

`PN=PE` 4.radius of same circle

5. ΔPEN is an Isosceles triangle,

∴ ∠ 1 ≅ ∠ 2 5. Isosceles triangle property

6. ∴ ∠5 ≅ ∠6 6. From 3 and 5 Transitive Property.........Proved