Circle stuff + coordinate geo proofs

A cirlce

is the set of all points that are equidistant from a fixed point called the center

Concentric circles

Two (or more) circles with the same center

A radius

is a segment from the center of the circle to a point on the circle

A chord

is a segment whose endpoints are on the circle.

A diameter

is a chord passing through the center of the cirlce

Notation: a lower case d

A diameter is equal to two radii (d = 2r)

A central angle

is an angle whose vertex is on the center of the circle.

An inscribed angle

is an agle whose vertex is on the circle

A secant

is a line that intersects a cirlce in two distinct points

A tangent

A tangent is a line that intersects a circle in exactly one point.

The point which the line intersects is called the point of tangency

NOTE: There is also tangent segments and rays!

360 degrees in a circle

180 in a semi circle

An arc

is part of the circle

The measure of an arc is in degrees and given by central angle that intercepts it

A minor arc

is an arc intercepted by a central angle smaller than 180, so its degree measure is less than 180

2 points

A major arc

is an arc intercepted by a central angle greater than 180 so its degree measure is greater than 180

3 points

2 line segments bisect each other

MP 2x (show midpoints are the same)

2 lines are perpendicular

slope 2x (show slopes are negative reciprocal)

2 lines are parallel to each other

slope 2x (show slopes are the same)

2 line segments are congruent

Distance 2x (show lengths are the same)

One line is a perpendicular bisector of a given line segment

slope 2x + MP 1x (Show that the line goes through the midpoint and that slopes are negative reciprocals

Altitude of a triangle

Slope 2x (show perpendicular by negative reciprocal)

Median of a triangle

MP 1x (show the line goes through the midpoints)

Isosceles triangle

2x distance (show 2 sides are congruent)

Right triangle

slope 2x (show negative reciprocal) or distance 3x (Pythagorean theorem)

Congruent triangles

Distance 6x (show triangles congruent by SSS)