Geometry Chapter 5 Theorems and Vocabulary

Flashcards for Geometry Chapter 5 Test

Perpendicular Bisector Theorem

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

Converse of the Perpendicular Bisector Theorem

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

Angle Bisector Theorem

If a point is on the bisector of an angle then the point is equidistant from the sides of an angle.

Converse of the Angle Bisector Theorem

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

Triangle Midsegment Theorem

If the segments join the midpoints of two sides of a triangle, then the segment is parallel to the third side and half as long.

Midsegment

A segment connecting the midpoints of two sides of a triangle.

Median

A segment whose endpoints are a vertex and the midpoint of the other side.

Concurrent

When 3 or more line intersect at one point.

Point of Concurrency

Point at which the lines intersect

Concurrency of Medians Theorem

The medians of a triangle are concurrent at a point that is two-thirds the distance from each vertex to the midpoints of the opposite sides.

Centroid

Point of concurrency of the medians.

• Always inside the triangle.

• AKA the center of gravity of the triangle.

Altitude

The perpendicular segment from a vertex of the triangle to the line containing the opposite side.

• Can be inside, outside, or an actual side of the triangle.

Orthocenter

Point of concurrency of the altitudes of a triangle.

• Can be inside, on, or outside of the triangle

Comparison Property of Inequality

If a = b + c and c > 0, then a > b

Corollary to the Triangle Exterior Angle Theorem

The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles.

If m1 = m2 + m3, then m1>m2 and m1>m3

Theorem 1 (Larger Angle)

If 2 sides of a triangle are not congruent than the larger angle lies opposite the longer side.

Theorem 2 (Longer side)

If 2 angles of a triangle are not congruent then the longer side lies opposite the larger angle.

Triangle Inequality Theorem

The sum of the lengths of any 2 sides of a triangle is greater than the length of the third side.

Range of possible lengths of the third side

The length of the third side of a triangle is greater than the difference in lengths of the other 2 sides, but less than the sum of the other 2 sides.

The Hinge Theorem

If 2 sides of one triangle are congruent to 2 sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle.

Converse of the Hinge Theorem

If 2 sides of one triangle are congruent to 2 sides of another triangle and the third sides are NOT congruent, then the larger included angle is opposite the longer side.