Geometry Dictionary: Angles

Angles

• An acute angle is less than 90 degrees but more than 0 degrees
• A right angle measures exactly 90 degrees
• An obtuse angle is more than 90 degrees but less than 180 degrees
• A straight angle measures exactly 180 degrees
• Vertical angles are congruent and across from each other when two lines intersect
• Adjacent angles share a common ray and vertex, and are next to each other
• Complementary angles have a sum of 90 degrees
• Supplementary angles have a sum of 180 degrees

Lines and Transversals

• Parallel lines never intersect
• A transversal is a line that intersects two or more lines
• Corresponding angles are in the same position on two parallel lines in relation to a transversal
• Alternate interior angles are inside the parallel lines and on opposite sides of the transversal
• Alternate exterior angles are outside the parallel lines and on opposite sides of the transversal
• Consecutive interior angles are inside the parallel lines and on the same side of the transversal, and their sum is 180 degrees

Triangles

• A triangle is a three-sided figure with a sum of three angles equal to 180 degrees
• An equilateral triangle has three congruent sides and three congruent angles
• An isosceles triangle has two congruent sides and two congruent angles
• A scalene triangle has no congruent sides or angles
• A right triangle contains a 90-degree angle
• The legs of a right triangle are the two sides that form the 90-degree angle
• The hypotenuse of a right triangle is the side opposite the right angle
• The Pythagorean theorem is a formula used to find sides of a right triangle

Quadrilaterals

• A quadrilateral is a four-sided figure with angles that sum to 360 degrees
• A parallelogram is a quadrilateral with opposite sides that are parallel and congruent
• A rhombus is a parallelogram with all four sides congruent
• A rectangle is a parallelogram with four right angles
• A square is a parallelogram with four congruent sides and four right angles
• A trapezoid is a quadrilateral with exactly one pair of parallel sides
• An isosceles trapezoid is a trapezoid with one pair of congruent sides

Polygons

• A polygon is a closed figure formed by three or more line segments called sides
• The sum of interior angles of a polygon can be determined by the number of triangles that can be drawn within the polygon
• Congruent polygons have the same size and shape
• A congruency statement must match all corresponding angles and sides

Transformations

• A transformation is an operation that maps an original figure (pre-image) onto a new figure (image)