Download Circle and Shape Properties to know

Diagram
Properties
If two chords are equidistant from the centre of a circle, then
the chords are congruent.
If
FO  EO
then
CD  AB
If two chords in a circle are congruent, then they are
equidistant from the centre of the circle.
If
CD  AB
then FO  EO
A line that is perpendicular to a chord and passes through the
centre of a circle bisects the chord.
A perpendicular bisector is a line that passes through the
midpoint of a line segment and is perpendicular to that line
segment.
Perpendicular bisectors of any two or more chords of a circle
pass through and intersect at the centre of that circle.
A line segment joining the midpoint of a chord and the centre
of the circle is perpendicular to the chord.
The measure of the minor arc is equal to the measure of the
central angle subtended by the arc.
A central angle is the angle with endpoints on the arc of a
circle and vertex at the centre.
The measure of the inscribed angle subtended by an arc is
equal to one-half the size of the arc.
An inscribed angle is the angle with endpoints on the arc of a
circle and vertex on the circumference of the circle.
The measure of the inscribed angle subtended by the same arc
as its central angle is equal in measure to one-half the measure
of the central angle.
An angle subtended by the diameter of a circle is always equal
to 900.
Two or more inscribed angles subtended by the same arc are
equal in measure.
If a quadrilateral is inscribed in a circle, it is called a cyclic
quadrilateral. Opposite angles in a cyclic quadrilateral are
supplementary (add to 1800).
A cyclic quadrilateral has all four vertices on the
circumference of the same circle..
A line drawn tangent to a circle meets the radius of the circle
at a right angle. A tangent to a circle is perpendicular to the
radius that meets it.
The measure of an angle between a tangent and a chord of a
circle is equal to the measure of the inscribed angle opposite
it.
A chord divides a circle into two arcs. The smaller arc is
called the minor arc. The larger arc is called the major arc.
The part of a circle that is formed by the arc and a chord is
called a segment.
Shape
Proof
Formulas to use
Rectangle
 Prove opposite sides are equal.
 Prove adjacent sides are perpendicular.
Distance formula
Slope formula
Square
 Prove opposite sides are equal.
 Prove adjacent sides are perpendicular.
Distance formula
Slope formula
Parallelogram
 Prove opposite sides are equal.
 Prove opposite sides are parallel
Distance formula
Slope formula
Rhombus
 Prove all sides are congruent.
 Prove opposite sides are parallel.
Distance formula
Slope formula
Trapezoid
 Prove one pair of opposite sides are
parallel.
Slope formula
Right Triangle
 Prove adjacent sides are perpendicular.
Slope formula
Isosceles Triangle
 Prove two sides are congruent.
Distance formula
Equilateral Triangle
 Prove three sides congruent.
Distance formula
Scalene Triangle
 Prove no sides congruent.
Distance formula