Right Angle
An angle that measures 90 degrees.
Acute Angle
An angle that measures between 0 and 90 degrees.
Obtuse Angle
An angle that measures between 90 and 180 degrees.
Acute Triangle
A triangle with three acute angles.
Obtuse Triangle
A triangle with one obtuse angle.
Right Triangle
A triangle with one right angle.
Equiangular Triangle
A triangle with three congruent angles.
Scalene Triangle
A triangle with no congruent sides.
Isosceles Triangle
A triangle with at least two congruent sides.
Equilateral Triangle
A triangle with three congruent sides.
Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180 degrees.
Exterior Angle
An angle formed by one side of a triangle and the extension of another side.
Remote Interior Angles
The angles of a triangle that are not adjacent to a given exterior angle.
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.
Angle Sum Corollary - Acute
The acute angles of a right triangle are complementary. That is, they add to 90 degrees.
Angle Sum Corollary - Right & Obtuse
The can be at most one right angle or one obtuse angle in a triangle.
Corresponding Parts
The matching sides and angles of two figures.
Congruent
Two or more figures that are the same size and shape. Sides are equal in length and angles are equal in measure.
Congruent Polygons
Two polygons are congruent if and only if their corresponding parts are congruent.
CPCTC
Corresponding Parts of Congruent Triangles are Congruent.
Third Angle Theorem
If two angle of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent.
Reflexive Property
?ABC ? ?ABC
Anything is equal to or congruent to itself.
Symmetric Property
If ?ABC ? ?EFG, then ?EFG ? ?ABC.
If one quantity equals or is congruent to a second quantity, then the second quantity equals or is congruent to the first.
Transitive Property
If ?ABC ? ? EFG and ?EFG ? ?JKL, then ?ABC ? ?JKL.
, If one quantity equals or is congruent to a second quantity, and the second quantity equals or is congruent to a third quantity, then the first quantity equals or is congruent to the third quantity.
SSS (Side-Side-Side) Congruence
If three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent.
Included Angle
An angle that is included between two sides of a triangle.
SAS (Side-Angle-Side) Congruence
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.
Included Side
A side included between two angles.
ASA (Angle-Side-Angle) Congruence
If two angles and the included side of one triangle are congruent to two angles and the included side of a second triangle, then the triangles are congruent.
AAS (Angle-Angle-Side) Congruence
If two angles and the non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.
Legs of an Isosceles Triangle
The two congruent sides of an isosceles triangle.
Vertex Angle of an Isosceles Triangle
The angle formed by the legs of an isosceles triangle.
Base Angles of an Isosceles Triangle
The two angles that are not the vertex angle of an isosceles triangle.
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.
Equilateral Triangle Property
A triangle is equilateral if and only if it is equiangular.
Angles of an Equilateral Triangle
Each angle of an equilateral triangle measures 60 degrees.