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# Math 4.1-4.7

### Math - Chapter 4 (4.1 - 4.7) Geometry

adjacent sides of a triangle Two sides of a triangle with a common vertex
corollary A statement that can be proved easily using a theorem or a definition
corollary to the triangle sum theorem The acute angles of a right triangle are complementary
exterior angles of a triangle When the sides of a triangle are extended, the angles that are adjacent to the interior angles
exterior angle theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles
interior angles of a triangle When the sides of a triangle are extended, the three original angles of a triangle
sides of an isosceles triangles The two congruent sides of an isosceles triangle are called the legs and the third side is known as the base
sides of a right triangle In a right triangle, the sides that form the right angle are called the legs and the side opposite the right angle is known as the hypotenuse
triangle A figure formed by three segments joining three noncollinear points called vertices.
equilateral triangle three congruent sides
isosceles triangle at least two congruent sides
scalene triangle no congruent sides
acute triangles three acute angles
equiangular three congruent angles
right triangle one right angle
obtuse triangle one obtuse triangle
triangle sum theorem the sum of the measures of the interior angles of a triangle is 180 degrees
vertex of a triangle each of the three points joining the sides of a triangle
congruent figures two geometric figures that have exactly the same size and shape. When two figures are congruent all pairs of corresponding angles and corresponding sides are congruent.
corresponding angles of congruent figures when two figures are congruent, the angles that are in corresponding positions and are congruent
corresponding sides of congruent figures when two figures are congruent the sides that are in corresponding positions and are congruent
reflexive property of congruent triangles every triangle is congruent to itself
symmetric property of congruent triangles if triangleABC is congruent to triangleDEF then triangleDEF is congruent to triangleABC
transitive property of congruent triangles If triangleABC is congruent to triangleDEF and triangleDEF is congruent to triangleJKL then triangleABC is congruent to triangleJKL
third angles theorem if two angles of one triangles are congruent to two angles of another triangle then the third angles are also congruent
SAS 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 two triangles are congruent
SSS congruence postulate if three sides of one triangle are congruent to three sides of a second triangle then the two triangles are congruent
AAS congruence theorem if two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of a second triangle then the two triangles are congruent
ASA congrunce postulate 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 two triangles are congruent
base angles of an isoceles triangle the two angles that contain the base of an isoceles
base angles theorem if two sides of a triangle are congruent, then the angles opposite them are congruent
corollary to base angles theorem if a triangle is equilateral, then it is equilangular
corollary to the converse of the base angles theorem if a triangle is equilangular, then it is equilateral
converse of the base angles theorem if two angles of a triangle are congruent, then the sides opposite them are congruent
hypotenuse-leg congruence theorem if the hypotenuse and the leg of a right triangle are congruent to the hypotenuse and a leg of a second right triangle, then the two triangles are congruent
vertex angle of an isoceles triangle the angle opposite the base of an isoceles triangle
coordinate proof a type of proof that involves placing geometric figures in a coordinate plane
Created by: jumpthemoon