congruent triangles

polygon

a closed figure made up of atleast 3 straight lines

triangle

a polygon with three sides

named by its vertices

always add to 180

3 sides, vertices, and angles

equilateral triangle

all sides are equal

also acute

isoscles

2 sides are equal

also equilangular

scalene

no equal sides

equilangular

all angles equal (60)

acute

all angles less than 90

obtuse

one angle greater than 90

right

1 angle equals 90

right triangle

hypotenuse and 2 legs

one right angle

isoscles triangle

1 base, 2 legs, vertex angle

triangle sum theory

the sum of the measure of the interior angles of a triangle is 180

exterior angle theory

the measure of the exterior angles of a triangle is equal to the sum of the measures of the 2 remote interior angles

corollary to triangle sum theory

the acute angles of a right triangle are complementary

base angle theory

if two sides of a triangle are congruent, then the angles opposite them are also congruent

converse of base angle theory

if two base angles of a triangle are congruent, then the two sides opposite them are also congruent

corollary to the base angle theory and corollary to the converse of the base angle theory

if a triangle is equilateral, then it is equilangular

distance formula

classify by sides of triangle

slope formula

determines if it is a right triangle (opposite recipricals)

naming a triangle by classification

2 broad names - side classification and angle classification