Triangle Angle Sum Theorem
The sum of the measures of the angles in a triangle is 180�
exterior angle of a triangle
the angle formed by one side of a triangle and the extension of its adjacent side
remote interior angles
the angles of a triangle that are not adjacent to the 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
corollary
a theorem that can be easily proved as a direct result of another theorem
Triangle angle sum corollary 4.1: The acute angles of a right triangle are ______________________.
complementary
Triangle angle sum corollary 4.2: There can be at most one right or _______________ angle in a triangle.
obtuse
congruent polygons
Polygons in which all pairs of corresponding parts (angles and sides) are congruent.
corresponding parts
parts (angles or sides) are in the same relative position in each of the figures
CPCTC
corresponding parts of congruent triangles are congruent
Third Angles Theorem
If two angles in one triangle are congruent to two angles in another triangle, then the third angles of the triangles are congruent
Side Side Side (SSS) Congruence Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent
included angle
an angle formed by two adjacent sides of a polygon
Side Angle Side Congruence Postulate
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 that is located between two consecutive angles
Angle Side Angle (ASA) Congruence Postulate
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent
Angle Angle Side (AAS) Theorem
If two angles and the nonincluded side of one triangle are congruent to two angles and the nonincluded side of another triangles, then the triangles are congruent.
Side Side Angle
SSA does NOT guarantee that the triangles are congruent
Angle Angle Angle
AAA does NOT guarantee that the triangles are congruent
Hypotenuse Leg (HL) Theorem
If the hypotenuse and a leg of one triangle are congruent to the hypotenuse and corresponding leg of another triangle, then the triangles are congruent. This is the one time that an SSA shortcut proves congruence.
isosceles triangle
a triangle that has at least two congruent sides
legs of an isosceles triangle
the congruent sides of an isosceles triangle
vertex angle of an isosceles triangle
the angle formed by the legs of an isosceles triangle
base of an isosceles triangle
the side opposite the vertex angle
base angles of an isosceles triangle
the two angles formed by the base and the congruent sides
Isosceles triangle theorem
If two sides of one triangle are congruent, then the angles opposite those sides are congruent.
Converse of the isosceles triangle theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
equilateral triangle
a triangle with all sides congruent
Equilateral Triangle Corollary: A triangle is equilateral if and only if it is __________________________.
equilangular
Equilateral Triangle Corollary: Each angle of an equilateral triangle measures ___________________
60 degrees