Geometry Final

circumcenter of a triangle

the point of concurrency of the three perpendicular bisectors of a triangle

orthocenter of a triangle

the point of concurrency of the three altitudes of a triangle

incenter of a triangle

the point of concurrency of the angle bisectors of a triangle

centroid of a triangle

The point of concurrency of the medians of a triangle

Distance formula

midpoint formula

slope formula

conditional statement

if p, then q

Converse Statement

If q, then p

Inverse Statement

If not p, then not q

Contrapositive Statement

If not q, then not p

adjacent angles

Two angles that share a common vertex and side

Linear Pair

Adjacent angles that are supplementary

Angle Bisector

A line, ray, or segment that divides an angle into two equal parts

Vertical Angles

Congruent Angles that are across from each other on intersecting lines

Perpendicular

Two lines that intersect at a 90 degree angle

Coplanar

Points that lie on the same plane

Ray

A line that extends indefinitely in one direction

Complementary Angles

Two angles with measures that have a sum of 90 degrees

Collinear

points that lie on the same line

Segment Bisector

a line, ray, or segment that divides a segment into two congruent segments

Supplementary Angles

two angles with measures that have a sum of 180

Line segment

A measurable part of a line consisting of two endpoints

1. 2(3x-5)=32
2. 3x-5=16

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Example of what property?

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Division Property of Equality

3. 3x-5=16
4. 3x=21

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Example of what property?

Addition Property of Equality

1. 2(3x-5)=32
2. 6x-10=32

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Example of what property?

Multiplication Property of Equality

1. 2x+5=10
2. 2x=5

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Example of what property?

Subtraction property of Equality

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Triangle Exterior Angle Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Perpendicular Bisector Theorem

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

Converse of the Perpendicular Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle

Angle Bisector Theorem

If a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle

Converse of the Angle Bisector Theorem

Concurrent

Three or more lines that intersect in one point (point of concurrency)

passes through all vertices of the triangle and contains the entire figure in its interior. The center of this circle is called the circumcenter

circumscribed circle of a triangle

a circle that is inside the triangle (center of the inscribed circle is the incenter)

inscribed circle

What is special about the Medians in the Centroid of a Triangle

Medians of a Triangle are concurrent at a point that is 2/3 the distance from each vertex to the midpoint of the opposite side.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Triangle Inequality Theorem

90 degree rotation counterclockwise

(x,y) —> (-y,x)

180 degree rotation counterclockwise

(x,y) —> (-x,-y)

270 degree rotation counterclockwise

(x,y) —> (y,-x)

Reflection of y=n

Horizontal flipping of shape (vertical line)

Reflection of x=n

Flipping of shape vertically (horizontal line)