Geometry Vocabulary Triangle Triangle: a polygon with three sides. 180 Sum of the interior angles of a triangle = 180 Acute Triangle Acute Triangle: a triangle in which all of the angles are less than 90. Obtuse Triangles Obtuse Triangles: A triangle with one angle that measures more than 90. Similar Triangles Similar Triangles: Triangles with congruent angles and proportional sides. Proportional : Proportional : Two variables which have a constant ratio between them. Right Triangle Right Triangle: A triangle that has one angle that equals 90. Hypotenuse: Hypotenuse: the longest side of a right triangle only. It is also the side directly across from the right angle. Legs: Legs: the sides of a right triangle that form the right angle. hypotenuse LegLeg Leg Leg Triangle: Triangle: In this triangle, the hypotenuse is twice the shorter leg and the longer leg is equal to the shorter leg time 3. Triangle: Triangle: In this triangle, the hypotenuse is equal to the leg multiplied by 2. Equilateral Triangle Equilateral Triangle: This is a triangle with all sides equal in length. Equiangular Triangle Equiangular Triangle: A triangle with all congruent angles. Isosceles Isosceles: This is a triangle with at least two congruent sides. Scalene Scalene: This is a triangle with three unequal sides. The mathematical relationship relating the three sides of a right triangle. a 2 + b 2 = c 2 Pythagorean Triple Pythagorean Triple: A set of 3 nonzero whole numbers that form the sides of a right triangle. (i.e. these numbers satisfy the formula a 2 + b 2 = c 2 ) Pythagorean Theorem Converse Pythagorean Theorem Converse: If the square of the length of the longest side of the triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle = 25 Polygon: Polygon: A closed plane figure formed by three or more line segments that do not cross over each other. Regular Polygon: Regular Polygon: A convex polygon with congruent angles and congruent sides. Concave means CAVED-in. Convex means curved-out. Quadrilateral Quadrilateral: A polygon with 4 sides. (i.e. square or rectangle) Cone Cone: This is a shape whose base is a circle and whose sides taper up to a point. Cylinder: Cylinder: This is a solid bounded by a curved lateral surface and two circular bases. Pyramid: Pyramid: This is a polyhedron having a polygon for a base and triangular sides with a common vertex. Prism: Prism: This is a solid with two parallel and congruent bases in the shape of polygons; the other faces are parallelograms. Rectangular Prism: Rectangular Prism: This is a solid figure where all sides are rectangles and all sides meet at right angles. Sphere Sphere: This is a round shell defined by a center point and a surface that lies at a constant distance from its center. Three-Dimensional Sphere Three-Dimensional Sphere: A three dimension solid that consists of all points equidistant from a given point. Angle Angle: These are two rays sharing a common endpoint. They are typically measured in degrees or radians. Vertex: Vertex: The point where the edges of a three dimensional figure intersect. (Also: A vertex is the maximum or minimum of a parabola, depending on whether the parabola opens up or down.) Adjacent Angles Adjacent Angles: These are two angles in a plane which share a common vertex and a common side but do not overlap. Corresponding Angles Corresponding Angles: These are two angles that are formed by two coplanar lines and a transversal. They occupy the same relative positions. Supplementary Angles Supplementary Angles: Two angles whose measure add up to 180 degrees. Complementary Angles Complementary Angles: These are a pair of angles, adjacent or nonadjacent, whose sum is 90 degrees. Vertical Angles Vertical Angles: These are angles opposite one another at the intersection of two lines. Congruent: Congruent: These are angles, segments, triangles, etc. that have exactly the same measures. Face: Face: One of the polygons that makes up a geometric solid. Edge Edge: The segment formed by the intersection of two faces in a geometric solid. Net: Net: A 2-dimensional representation of a 3-dimensional figure. (Illustration on next slide) Edge Face Sum of Interior Angles of a Polygon Sum of Interior Angles of a Polygon: This sum is found by subtracting 2 from the number of sides and then multiplying by 180. m = 180 (n 2) Where: m = the measure of the sum of the interior angles and n = the number of sides of the polygon