Question

State and prove exterior angle property of triangles tate and prove exterior angle property of a triangle

Answer 1

Exterior angle property

Exterior and interior opposite angle

In a triangle is a side of a triangle is produced in

either direction the angles so formed with any of

the other side is called the exterior angle of the

triangle. The angle inside the triangle opposite of

the exterior angles so formed are called the

interior opposite angle.

the arms on<AXD in your notebook.

Thus, we can see that <ACD=<A+<B

Thus, we can see that <ACD=<A+<BThis verify that the exterior angle of the triangle

Thus, we can see that <ACD=<A+<BThis verify that the exterior angle of the triangle is equal to the sum of the interior positive angle.

Proof of exterior angle property.

In ∆PQR,side PR is produced to S, forming an

exterior angle QRS.<1 and <3 are interior positive angle.

<1+<2+<3=180°(angle sum property)

<4+<2=189°(Linear pair)

So,

<1+<2+<3=<4+<2. [By using (1) and (2)]

therefore

<1+<3=<4+<2

or

<4=<1+<3

Thus,the exterior angle is equal to the sum of the interior opposite angle.