Plane Geometry
1. Supplementary Angles
 two angles add up to 180º
2. Complementary Angles
 Angles that add up to 90º
3. Opposite angle theorem

4. The sum of Interior angles of a triangle
 The three angles always add to 180°
Equilateral
Triangle
Three equal sides
Three equal angles,
always 60°
Isosceles Triangle
Two equal sides
Two equal angles
Scalene Triangle
No equal sides
No equal angles
Any straight line that is
intersected by another line will
produce angles, when opposite
one another that are equal in
degrees
Acute Triangle
All angles are less than
90°
5. Exterior angle theorem
 the measure of an exterior angle of
a triangle is equal to the sum of the
measures of the two remote
interior angles.
6. Parallel line Theorem
 When a transversal intersects
two parallel lines :
Right Triangle
Has a right angle (90°)
Obtuse Triangle
Has an angle more than
90°
* two angles in each pair of alternate
angles are equal (Z shape -i.e. C and
F are equal and D and E are equal)
* two angles in each pair of
corresponding angles are equal (F
shape – B and F are equal, D and H
are equal)
* the interior angles are
supplementary (C shape – D and F
equals 180º)
7. Sum of interior angles of polygons
 The interior angles of any polygon always add up to a constant value, which
depends only on the number of sides
The sum of the interior angles of a polygon is given by the formula
sum  180(n  2) deg rees
where
n is the number of sides
So for example:
A square has 4 sides, so interior angles add up to 360°
A pentagon has 5 sides, so interior angles add up to 540°
A hexagon has 6 sides, so interior angles add up to 720°

For regular polygons (those with all the angles the same value) the value of
each angle is given by:
180(n  2)
deg rees
n
where
n is the number of sides