FINAL #1, Geometry

30 terms

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180°.

Exterior Angles Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Corollary to the

Third Angles Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. Properties of Congruent Triangles.

Reflexive Property of Congruent Triangles

Every triangle is congruent to itself.

Transitive Property

If A=B, and B=C, then A=C.

A=B, B=A.

A=A.

SSS

If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

SAS

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

ASA

If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the two triangles are congruent.

AAS

If two angles and a nonincluded side of one triangle are congruent to two angles and a nonincluded side of a second triangle, then the two angles are congruent.

Base Angles Theorem

If two sides of a triangle are congruent, then the angles opposite them are congruent.

Hypotenuse-Leg (HL) Congruence Theorem

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent.

Perpendicular Bisector Theorem

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

Angle Bisector Theorem

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

Concurrent Lines

Lines that intersect at the same point.

Circumcenter

The point of concurrency of the perpendicular bisectors of a triangle. Equidistant from the vertices of a triangle.

Incenter

The point of concurrency of the angle bisectors of a triangle. ALWAYS inside the triangle. Equidistant from the sides of the triangle.

Centroid

The point of concurrency where segments whose endpoints are a vertex of the triangle and the midpoint of the opposite side meet. 2/3 of the distance from each side.

Orthocenter

A line perpendicular to one side, and passes through the opposite vertex.

Midsegment Theorem

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.

A Theorem

If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

A Theorem

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle

Triangle Inequality

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

Hinge Theorem

If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second. (Know the Converse)

A Theorem

If a quadrilateral is a parallelogram, then its opposite sides are congruent. (Same for angles)

A Theorem

If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

A Theorem

If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Midsegment Theorem for Trapezoids

The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases.

Kite

A quadrilateral with two pairs of consecutive sides, but opposite sides are not congruent. (diagonals perpendicular, one pair of congruent opposite angles).