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Diagram GEOMETRY FACT ANGLE RELATIONSHIP NAME Vertical angles are congruent and opposite each other, formed by 2 intersecting lines. Vertical Angle vert. s a b or ma mb Angles on a Line/ Parts of a straight angle The sum of the adjacent angles on a line is 180⁰. Adjacent angles: angles next to each other sharing a 1 side C D b° a° c° A B Angles on a Line s on a line E BAC CAD DAE 180 Straight angle: an angle of 180⁰ with 2 sides facing in opposite directions. Supplementary angles: two angles that form a linear pair that have a sum of 180.⁰ One angle is a supplement of the other angle. a b c 180 ao SUPPLEMENTARY ANGLES bo 𝒂 + 𝒃 = 𝟏𝟖𝟎 (2 Angles on a Line) Supplementary angles add to 180⁰. Angles at a Point: sum of the measures of all angles formed by three or more rays with the same vertex is 360˚. Angles at a Point s at a point ABC DBC CBA 360 B Angle Sum of a Triangle: the sum of the 3 interior angles of any triangle is 180˚. C A Angle Sum of a Triangle sum of A B C 180 Exterior angle of a triangle is equal to the sum of the measures of two opposite interior angles of a triangle. Exterior Angle of a Triangle ext. of Exterior angle is formed by extending one of the sides of the triangle. A C BDC Angle sum of a Right Triangle: when one angle of a triangle is a right angle, the sum of the measures of the other two angles is 90˚. Complementary angles: two angles with a sum of 90˚. Angle sum of a Right Triangle sum of rt. COMPLEMENTARY ANGLES Diagram GEOMETRY FACT Perpendicular lines: when two lines lie in the same plane and intersect to form right angles. ANGLE RELATIONSHIP NAME Perpendicular Lines Q. F • G • QR FG .R Parallel lines: two lines that lie in the same plane that never intersect and are the same distance apart. Line m1 is parallel to m2 Parallel Lines m1 / / m2 Equidistant: 2 objects the same distance apart Corresponding Angles: when a transversal intersects two parallel lines then the measures of the corresponding angles are equal. Corresponding angles Same side of transversal Same side of 2 // lines Converse: If a transversal intersects two lines such that the measures of the corresponding angles are equal, then the lines are parallel. Alternate Interior Angles: when a transversal intersects two parallel lines, then the measures of alternate interior angles are equal. Alternate Interior Angles Opposite sides of transversal In-between the 2 // lines Converse: If a transversal intersects two lines such that measures of the alternate interior angles are equal, then the lines are parallel. Alternate Exterior Angles: when a transversal intersects two parallel lines, then the measures of alternate exterior angles are equal. Alternate Exterior Angles Opposite sides of transversal Outside of the 2 // lines Converse: If a transversal intersects two lines such that measures of the alternate exterior angles are equal, then the lines are parallel. If a transversal intersects two parallel lines, any pair of angles is either CONGRUENT or SUPPLEMENTARY equal in measure or add to 180⁰ If a and b are created by parallel lines cut by a transversal, then a + b 180 or a b General understanding of Parallel Lines angle relationships