20 terms

Chapter 4 (McDougall Littell) Geometry terms, theorems, postulates, etc.

Triangle Inequality Theorem

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

congruent polygons

are congruent only if all corresponding parts are congruent

corresponding part

the part of one shape has to be congruent to that same corner on the other shape

SSS

If three sides of a triangle are congruent to three sides of another triangle, then the triangles are congruent

SAS

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

ASA

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

AAS

If two angles and a NON-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent

HL

If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent. *Only for use of right triangles

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then the point is an equal distance from the endpoints of the segment

legs of isosceles triangle

are opposite base

base of isosceles triangle

opposite two legs

base angle of isosceles triangle

congruent angles on the base

vertex angle

point at which the two legs meet (opposite base)

Isosceles Triangle Theorem

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

Converse of Isosceles Triangle Theorem

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

median of a triangle

a segment from a vertex to the midpoint of the opposite side

altitude of a triangle

perpendicular segment from a vertex to the line that contains the opposite side

SSA

Side-side-angle does NOT prove triangle congruence; exception is with a right triangle (see HL)

CPCTC

Corresponding parts of congruent triangles are congruent; once two triangles have been proven congruent (by using SSS, SAS, ASA, AAS, or HL), then we can conclude its parts are congruent through CPCTC

AAA

Angle-angle-angle does NOT prove triangle congruence (however, triangles will be similar; only need AA to prove similarity)