unit 3 (proofs) terms and definitions

unit 3 - triangles

triangle

a shape formed by three segments joining three noncollinear points

scalene

no congruent sides

isosceles

two congruent sides

equilateral

all sides are congruent (also an equiangular)

equiangular

all angles are congruent (=60) ((also an equilateral))

acute

all angles are acute

obtuse

one angle is obtuse

right

one angle is right

angles sum theorem

the sum of the measures of the angles of a triangle is 180

corollary of a theorem

a statement that can be proved by applying a theorem or can be used as a reason in a proof

corollaries of angle sum theorem

\-each angle of an equiangular triangle has measures of 60

\-the acute angles of a right angle are complementary

\-there can be, at most, one right or obtuse angle in a triangle

third angle theorem

if two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent

exterior angle theorem

the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles

CPCTC

Congruent Parts of Congruent Triangles are Congruent

SSS Postulate

If the sides of one triangle are congruent to the corresponding sides of a second triangle, then the triangles are congruent

SAS Postulate

If two sides and the included angle (the one in between) of one triangle are congruent to the corresponding two sides and the included angle (the one in between) of another triangle, then the triangles are congruent

ASA Postulate

If two angles and the included side (the one in between) of one triangle are congruent to the corresponding two angles and the included side (the one in between) of another triangle, then the triangles are congruent

dialation

not congruent (size of sides and angles change)

translation

congruent (location change (up, down, right, left, etc.))

reflection

congruent (location change (flipped) (right, left, up, down, etc))

rotation

congruent (location change (right and left))

isosceles triangle theorem

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

converse of isosceles triangle theorem

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

AAS Theorem

if two angles and the non-included side of one triangle are congruent to the corresponding angles and side of a second triangle, then the two triangles are congruent

hypotenuse leg theorem

if the hypotenuse and a leg of one right triangle are congruent to the corresponding hypotenuse and leg of another right triangle, then the two triangles are congruent