Geometric Proof

GCSE Higher

Prove that the sum of the angles in a triangle is 180°

A

C

B

We can use previousknowledge of the properties ofparallel lines

EXTEND the line AB to a point G

G

DRAW line BE parallel to AC

E

Prove that the sum of the angles in a triangle is 180°

A

C

B G

E

<ACB = <CBE Alternate Angles

<CAB = <EBG Corresponding Angles

<CBA + <CBE + <EBG = 180º Angles on a straight line

SO <CBA + <ACB + <CAB = 180º

The Angle Sum of a triangle is 180º

Using this …

…could you prove that the exterior angle of a triangle is equal to the sum of the two opposite interior angles?