Complementary angles two angles whose sum of angle measures equals 90 degrees – Supplementary angles two angles whose sum of angle measures equals 180 degrees – Triangle a polygon with three sides and three vertices – Interior angles of a triangle angles that are inside of a triangle, formed by two sides of the triangle – Ex: Exterior angles of a triangle angles that are outside of a triangle between one side of a triangle and the extension of the adjacent side – Ex: Informal arguments to establish facts about triangles The sum of the measures of the interior angles of a triangle equals 180º. Adjacent interior and exterior angles create a supplementary pair of angles (the sum of the measures equals 180º). An exterior angle is equal to the sum of the two non-adjacent interior angles or the remote interior angles. The sum of the measures of the exterior angles, one at each vertex, of a triangle equals 360°. Ex: Congruent angles angles whose angle measurements are equal – Arc(s) on angles are usually used to indicate congruency. Vertical angles a pair of non-overlapping angles that are opposite and congruent to each other when two lines intersect – Ex: Parallel lines lines that lie in the same plane, never intersect, and are always the same distance apart – Various orientations including vertical, horizontal, diagonal, and parallel lines of even, uneven, or off-set lengths Lines that are parallel may or may not contain parallel markings. Ex: Transversal a line that intersects two or more lines – Ex: Alternate interior angles When two parallel lines are cut by a transversal, alternate interior angles are formed on opposite sides of the transversal and on the inside of the parallel lines. Ex: Alternate exterior angles When two parallel lines are cut by a transversal, alternate exterior angles are formed on opposite sides of the transversal and on the outside of the parallel lines.
Complementary angles – two angles whose sum of angle measures equals 90 degrees Supplementary angles – two angles whose sum of angle measures equals 180 degrees Triangle – a polygon with three sides and three vertices Interior angles of a triangle – angles that are inside of a triangle, formed by two sides of the triangle Ex: Exterior angles of a triangle – angles that are outside of a triangle between one side of a triangle and the extension of the adjacent side Ex: Informal arguments to establish facts about triangles The sum of the measures of the interior angles of a triangle equals 180º. Adjacent interior and exterior angles create a supplementary pair of angles (the sum of the measures equals 180º). An exterior angle is equal to the sum of the two non-adjacent interior angles or the remote interior angles. The sum of the measures of the exterior angles, one at each vertex, of a triangle equals 360°. Ex: Congruent angles – angles whose angle measurements are equal Arc(s) on angles are usually used to indicate congruency. Vertical angles – a pair of non-overlapping angles that are opposite and congruent to each other when two lines intersect Ex: Parallel lines – lines that lie in the same plane, never intersect, and are always the same distance apart Various orientations including vertical, horizontal, diagonal, and parallel lines of even, uneven, or off-set lengths Lines that are parallel may or may not contain parallel markings. Ex: Transversal – a line that intersects two or more lines Ex: Alternate interior angles When two parallel lines are cut by a transversal, alternate interior angles are formed on opposite sides of the transversal and on the inside of the parallel lines. Ex: Alternate exterior angles When two parallel lines are cut by a transversal, alternate exterior angles are formed on opposite sides of the transversal and on the outside of the parallel lines.