Angle Sum Theorem

In a triangle the sum of all the three interior angles will be equal to 180^o.  If one side of a triangle is produced, the exterior angle so formed is equal to the sum of the interior opposite angles. Here we are going to see about the angle sum theorem.

Understanding Angle Bisector Theorem is always challenging for me but thanks to all math help websites to help me out.

Angle sum theorem:

Angle sum theorem of a triangle is equal to two right angles, i.e., 180 degrees
Given:
ABC is a triangle
To Prove
Angle A + Angle B + Angle ACB = 180^o
Produce BC to D. Through C draw CE || BA.

Proof of angle sum theorem of a Triangle:

Statement	Reason
1. Angle A = Angle ACE	Alternate angles angles BA is parallel to CE
2. Angle B = Angle ECD	Corresponding angles BA is parallel to CE
3. Angle A + angle B = Angle ACE + Angle ECD	statements (1) and (2)
4. Angle A + angle B  = Angle ACD	statement (3)
5. Angle A + Angle B + Angle ACB = Angle ACD + Angle   ACB	adding Angle ACB to both sides
6. But Angle ACD + Angle ACB = 180o	linear pair
7. Angle A + Angle B + Angle ACB = 180 °	statements (5) and (6)

I am planning to write more post on Circle Circumference, cbse vi question papers. Keep checking my blog.

Corollary of Theorem on Angle theorem of a Triangle

If one side of a triangle is produced, the exterior angle so formed is equal to the sum of the interior opposite angles.
Given:
In Triangle ABC, BC is produced to D.
To Prove Corollary of Sum of Angles of Triangle:
Angle ACD = Angle A + Angle B



Proof:

Statement	Reason
1. Angle ACB + Angle ACD = 180o.	linear pair
2. Angle A + Angle B + Angle ACB = 180o	sum of the angles of a triangle = 180
3.  Angle ACB + Angle ACD = Angle A + Angle B + Angle ACB	statements (1) and (2)
4. Angle ACD = Angle A + Angle B Reason	statement (3); Angle ACB is common