Geometry Chapter 6 Test

Equidistant

Same distance from two figures

Perpendicular Bisector Theorem

If a point lies on a Perpendicular Bisector then it is equidistant from the endpoints of a segment

Perpendicular Bisector

A bisecting line that is perpendicular to the line it is cutting

Converse PB Theorem

If a point is equidistant from the end points of a segment then it lies on the Perpendicular Bisector

Angle Bisector

A Bisector of an angle that creates two identical angles

Angle Bisector Theorem

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

Converse AB Theorem

If a point is on the interior angle and equidistant from the sides of the angle then it lies on the Angle Bisector

Concurrent Lines

When 3 or more lines intersect at the same point

Point of Concurrency

The point that concurrent lines meet on

Circumcenter

The point of concurrency in a triangle

Circumcenter Theorem

If perpendicular bisector of a triangle intersect at a point, that point in the circumcenter which is equidistant from the vertices of said triangle

Incenter

Point of Concurrency for angle bisectors

Incenter Theorem

The incenter is equidistant from all sides

Median

Segment from vertex to midpoint of opposite side

Centroid

Point of Concurrency for medians

Centroid Theorem

The centroid of a triangle is 2/3rds of the distance from each vertex to midpoint

Orthocenter

Point of concurrency of altitudes

Altitude

From a vertex to the opposite side at a right angle

Midsegment

Segment that connects the two midpoints of a triangle

Triangle Midsegment Theorem

The midsegment connecting two midpoints is parallel and ½ the size of the opposite side

Hinge Theorem

If two triangles have two congruent sides but one of the angles between the congruent sides is larger than the other, the side across from it will always be longer than the other triangle’s third side

Hinge Converse

If two sides of a triangle are congruent, the angle across from the third side that is longer will be larger than the other triangle’s angle

Indirect Proof

Assume the opposite of what you are trying to prove, continue through proof until contradiction is found

Triangle Inequality Theorem

Sum of any 2 sides of a triangle is larger than the third side