Theorem 6

Question 1

Theorem

Answer 1

Each exterior angle of a triangle is equal to the sum of the two interior opposite angles

Question 2

Given

Answer 2

A triangle ABC with the side [bc] extended to the point D.

The angles are marked 1,2,3 and 4 are also given

Question 3

Required to prove

Answer 3

|<4| = |<1| + |<2|

Question 4

Proof

Answer 4

|<3| + |<4| = 180° …..straight angle
|<1| + |<2| + |<3| = 180° …angles in a triangle
.: |<3| + |<4| = |<1| + |<2| + |<3|
.: |<4| = |<1| + |<2| ….subtract |<3| from both sides