Geometry and Trig Chapter 3 vocab

Congruent figures

two or more figures with the same shape & size

Triangle

a 3 sided polygon

6 parts of a triangle

3 angles and 3 sides

congruent polygons

all pairs of corresponding parts (sides/angles) are congruent

congruent triangles

all 6 pairs of parts of a triangle are congruent

reflexive property

an angle or segment is congruent to itself

included angle

angle formed by 2 sides of a triangle

included sides

the common side between 2 angles of a triangle

Side Side Side Postulate

if 3 sides of a triangle are congruent to the corresponding 3 sides of a 2nd triangle then the triangles are congruent

Side Angle Side Postulate

if 2 sides and their included angle of a triangle are congruent to the corresponding 2 sides and their included angle of a 2nd triangle then the triangles are congruent

Angle Side Angle Postulate

if 2 angels and their included side of a triangle are congruent to the corresponding 2 angles and their included angle of a 2nd triangle then the triangles are congruent

CPCTC

Corresponding Parts Congruent Triangles Congruent

Circle

an infinite collection of points that are the same distance from a central point (known as the center)

Center

The point at the same distance from all the points of a circle

radius

a segment with an endpoint on a circle and an endpoint that is the center of the circle

Circumference

C = 2πr

Area

A = πr^2

types of triangles

Scalene, Isosceles, equilateral, and equiangular

Scalene triangle

A triangle with no congruent sides

Isosceles triangle

A triangle with at least 2 congruent sides

Equilateral triangle

A triangle with all 3 sides congruent

Equiangular triangle

a triangle with all 3 angles congruent

legs of isosceles triangle

Congruent sides of isosceles triangles

base of isosceles triangle

non-congruent side of isosceles triangle

Vertex angles

angle of an isosceles triangle when sides are the legs of the triangle

Base angles

angles of an isosceles triangle who have the base as one of their sides

Angle classification

acute, right, and obtuse

acute

A triangle which has 3 acute angles

right

a triangle with exactly one right angle

obtuse

a triangle with exactly 1 obtuse angle

triangle sum theorem

the measure of the 3 interior angles of a triangle sum to 180 degrees

No choice theorem

if 2 angles form one triangle congruent to the 2 angles in the second triangle the pair of angles are congruent

Angle Angle Side Postulate

if two angles and one side form a triangle congruent to the two angels and side in the second triangle the triangles are congruent

Hypotenuse

side opposite the right angle in a right triangle

legs of a right triangle

two side in a right triangle that form the right angle

median

a segment drawn from the vortex of a triangle to the midpoint of the opposite side

altitude

a segment drawn from the vortex of a triangle perpendicular to the opposite side (extend if necessary)

Angle side

- if two sides in a triangle are congruent then the angles opposite those sides are also congruent - if two angles in a triangle are congruent then the sides opposite them are congrurent

Angle side for Scalene triangles

- if two sides of a triangle are not congruent, then the angles opposite then are also not congruent and the larger angle is opposite the larger side - if two angles of a triangle are not congruent, then the sides opposite of them are also not congruent and the longer side is opposite if the larger angle

Hypotenuse leg Postulate

if the hypotenuse and a leg of a right triangle are congruent to the corresponding hypotenuse and leg of a 2nd right triangle then the triangles are congruent

auxiliary lines postulate

2 points that make a segment