Unit 4 Triangles and Congruence Vocab

Polygon

a closed 2d shape with at least 3 straight sides

Interior angles

angles on the inside of a polygon

Vertex

a point where 2 lines intersect, "corner"

Triangle Sum Theorem

the angles of a triangle add up to 180 degrees

Equiangular Triangle Theorem

If all 3 angles are congruent in a triangle, then each measures 60 degrees

Theorem related to right triangles

If there is a right triangle, then the 2 non-right angles are complementary

Acute Triangle

all 3 angles are less than 90 degrees

Right Triangle

exactly one angle tat measures 90 degrees

Obtuse Triangle

exactly one angle that measures greater than 90 degrees

Equiangular Triangle

all 3 angles are congruent

Equilateral Triangle

all 3 sides are congruent

Isosceles Triangle

at least 2 congruent sides

Scalene Triangle

no sides are congruent

Exterior Angles

angles outside of a triangle, each one forms a linear pair with the interior angle

Exterior Angle Sum Theorem

The sum of each set of exterior angles is 360 degrees

Remote Interior Angles

given an exterior angle, they are the non adjacent interior angles

Adjacent Interior Angles

given an exterior angle, the interior angle that forms a linear pair

Exterior Angle Theorem

the exterior angle is equal to the sum of the remote interior angles

Triangle Congruence

when 2 or more triangles have all congruent angles and all congruent sides

Third Angle Theorem

Given two triangles, if 2 sets of angles are congruent, then the third set of angles are congruent

SSS Triangle Congruence Postulate

Given 2 triangles, if all 3 sets are congruent, then the triangles are congruent

Included Angle

given two sides, the angle at the intersection, "in between"

SAS Triangle Congruence Postulate

Given 2 sets of congruent sides and congruent included angles, then the triangles are congruent

ASA Triangle Congruence Postulute

Given 2 sets of congruent angles and congruent included sides, the triangles are congruent

AAS Triangle Side Congruence Theorem

Given 2 sets of congruent angles and a not included side, then the triangles are congruent

Hypotenuse Leg Theorem

Given 2 RIGHT triangles, if one set of legs are congruent, and the hypotenuses are congruent, then the triangles are congruent

CPCTC

corresponding parts of congruent triangles are congruent

Isosceles Triangles

a triangle with 2 or more congruent sides

Base Angle Theorem

If there is an isosceles triangle, then the base angles are congruent

Isosceles Triangle Theorem

The angle bisector of the vertex is also the perpendicular bisector of the base

Equilateral Triangle Theorem

If a triangle is equilateral, then it is equiangular