Triangle Proofs

interior angles

angles inside a polygon

exterior angles

exterior angle and its adjacent interior angle are supplementary

triangle inequality theorem

the sum of the 2 smaller sides of a triangle has to be greater than the measure of the 3rd side

triangle angle sum theorem

the angles of a triangle add to 180

scalene

no equal sides

isosceles

2 equal sides

equilateral

all equal sides

acute

all angles in a triangle are less than 90

right 

one right angle in a triangle

obtuse

one obtuse angle in a triangle

largest angle

opposite largest side

smallest angle

opposite smallest side

if 2 sides are congruent

their opposite angles are congruent

isosceles triangle theorem

if two sides of a triangle are congruent, then their opposite sides are congruent

converse of the isosceles triangle theorem

if two angles of a triangle are congruent, then their opposite sides are congruent.

equilateral triangles

all sides are congruent, therefore all angles are congruent

midpoint

point located in the middle of a segment

angle bisector

line, segment, ray, etc. that goes through an angle at its midpoint

perpendicular bisector

line, segment, ray, etc. that forms right angles at the midpoint of a segment

segment bisector

line, segment, ray, etc. that intersects a segment at its midpoint

median

a segment in a triangle that connects the midpoint of a side to the opposite vertex

CPCTC

if triangles are congruent, then all the corresponding parts are congruent

SSS

all 3 sides are equal

SAS

two sides and the included angle are equal

ASA

two angles and the included side are equal

AAS

two angles and the non included side are equal

included angle

between the congruent sides

non included angle

not between the two congruent sides

included side

between the two congruent angles

non included side

not between the two congruent angles