Geometry 4

The Distance Formula

formula for distance between points

Definition of polygon

A polygon is a connected set of at least three line segments in the same plane such that each segment intersects exactly two others, one at each endpoint

congruent polygons

same size and shape

congruent triangles

Two triangles are congruent iff there is a correspondence between their vertices such that all of their corresponding sides and angles are equal

Corollary to the definition of congruent triangles

Two triangles congruent to a third triangle are congruent to each other

Postulate 5- The ASA Postulate

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

Postulate 6- The SAS Postulate

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

CPCTC definition

Congruent pats of congruent triangles are congruent/equal

Definitions of scalene, isosceles, and equilateral

A triangle is

scalene iff it has no equal sides

isosceles iff it has at least 2 equal sides

equilateral iff all of its sides are equal

Definition of obtuse, right, actute, and equiangular

A triangle is

obtuse iff it has an obtuse angle

right iff it has a right angle

acute iff all of its angles are acute

equiangular iff all of its angles are equal

Thereom 9

If two sides of triangle are equal, the angles opposite them are equal.

Theorem 10

If two angles of a triangle are equal, the sides opposite them are equal

Corollaries to Theorem 9 and 10

An equilateral triangle is equiangular

An equiangular triangle is equilateral

Theorem 11. The SSS Theorem

If three sides of one triangle are equal to the three sides of another triangle, the triangles are congruent