Math 12AP – Reviewing of Circle Geometry Topics

 

Chord Properties

• Congruent chords are located the same distance away from the centre of a circle.
• The perpendicular bisector of a chord passes through the centre of a circle.
• The longest chord in a circle is the diameter.

 

Logic Statements

• An “if and only if” statement (iff) can be made if the original statement and the converse of that statement are both true.

 

Coordinate Geometry

• Parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes
• Pythagorean Theorem
• Distance Formula
• Midpoint Formula
• Know how to find the centre of a circle given the endpoints of two chords on the circle.
• Know how to find the area of a triangle given the vertices of a triangle by finding an altitude.

 

Congruent Triangles and Proofs

• SSS, SAS, ASA, SAA and HL Triangle Congruence Theorems
• Two column proofs.  Justifications for statements in a proof might include shared side, segment addition, supplementary or complementary angles, x-theorem (vertical angles are congruent), z-theorem (opposite interior angles are congruent), definitions of midpoint, isosceles, or perpendicular.

 

Central and Inscribed Angle Properties

• The measure of a central angle is equal to the measure of the arc it intercepts.
• An inscribed angle is half the measure of the central angle subtended by the same arc.
• All inscribed angles subtended by the same arc are equal.
• An angle inscribed in a semi-circle measures 90°.

 

The Equation of a Circle

• Standard Form is  for a circle with centre (h, k) and a radius of r.
• General Form is
• Transformational Form is  for a circle with centre (h, k) and a radius of r.
• Mapping rules as transformations of the unit circle
• Graphing circles from their equation and stating the domain and range

 

The Equation of an Ellipse

• An ellipse is a circle that has been stretched horizontally and vertically by different amounts.
• Transformational form is  for an ellipse with centre (h, k).  2a is the length of the horizontal axis of the ellipse and 2b is the length of the vertical axis.
• The longer axis of an ellipse is called the major axis, and the shorter axis is called the minor axis.