Plane Geometry
Types of Angles
Acute angles- 0 ° to 89 °
Right Angle- 90 °
Complementary Angle- an angle whose
sum is 90 °
Obtuse Angle- greater than 90 ° but less
than 180 °
Straight Angle- 180 °
Supplementary Angle- angle whose sum is
180 °
Reflex Angle- greater than 180 ° but less
than 360 °
Angle of Revolution- 360 °
Example
Vertically opposite angles are equal
Angles at a point add up to 360°
Parallel Lines
Alternate angles are equal
Corresponding angles are equal
Co-interior angles are supplementary
Intercepts- a family of parallel lines cuts
all transversals in the same ration a:b=c:d
or a/b=c/d
Examples
Types of Triangles
Scalene triangle has no two sides equal in
length or two angles the same size
Right angle triangle
Isosceles triangle has two equal sides and
the two base angles are the same size
Equilateral triangle has all sides and
angles equal
Interior angle sum of a triangle is 180°
Exterior angle sum of any triangle is
equal to the two interior opposite angles
Examples
Congruency Tests
SSS: all corresponding sides are equal
SAS: 2 pairs of corresponding sides are
equal and their included angle is equal
AAS: 2 pairs of corresponding angles are
equal and included corresponding side is
equal
RHS: both triangles have a right angle;
their hypotenuses are equal and 1 other
pair of corresponding angles are equal
Examples
Types of quadrilaterals
Parallelogram: a quadrilateral with both
pairs of opposite sides parallel
Properties/tests
Properties
 Opposite sides are equal
 Opposite angles are equal
 Diagonals bisect each other
 Each diagonal bisects the parallelogram
into two congruent triangles
Tests
 Both pairs of opposite sides are equal
 Both pairs of opposite angles are equal
 One pair of sides are both equal and
parallel
 Diagonals bisect each other
Rectangle: a parallelogram where all angles
are right angles
Properties (has all properties of a
parallelogram):
 Diagonals are equal
Test
 A quadrilateral is a rectangle if its
diagonals are equal
Properties (has all properties of a
parallelogram):
 Diagonals bisect at right angles
 Diagonals bisect the angles they make
with the sides
Tests
 All sides are equal
 Diagonals bisect each other at right
angles
Properties (has all the properties of a
rectangle)
 Diagonals are perpendicular
 Diagonals make angles of 45° with the
sides
Rhombus: a parallelogram with a pair of
adjacent sides equal
Square: a rectangle with a pair of adjacent
sides equal
Trapezium: a quadrilateral with 1 pair of
sides parallel
Kite: a quadrilateral with 2 pairs of adjacent
sides equal
Shape
Rectangle
Square
Triangle
Parallelogram
Rhombus
Trapezium
Circle
Area formula
A=l b
A=s2
A=1/2 b h
A=b h
A=1/2
A=1/2
Similar Triangle theorem
Example
Two angles of one triangle are equal to two
angles of the other triangle
The ratio between two sides of one triangle
is equal to the ratio between the
corresponding sides of the other triangle
and the enclosed angles are equal
The ratios of corresponding sides are
equal
Pythagoras’ theorem
Polygon angle sum
Theorem
Interior angle sum
Exterior angle sum
Intercepts on transversals theorems
If a family of parallel lines cuts off equal
intercepts on one transversal, then it cuts
off equal intercepts on all transversals
The intercepts on all transversals by a
family of parallel lines are in the same
ratio
The line through the midpoint of one side
of a triangle parallel to another side
bisects the third side
A line parallel to one side of a triangle
divides the other sides in proportion
The line joining the midpoints of two sides
of a triangle is parallel to the third side
and half its length
Examples