Line: It s a straight arrangement of points that extends indefinitely in opposite directions.
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1 More Terminology and Notation: Plane: It s an infinitely large flat surface. Line: It s a straight arrangement of points that extends indefinitely in opposite directions. ollinear Points: Points that lie on the same line are called collinear points. D oncurrent Lines: Three or more lines that contain the same point are called concurrent.
2 Line Segment: It s the straight arrangement of points that connect two points called the endpoints. Midpoint: It s the point on a line segment that is equidistant from the endpoints. d d Ray: It s a straight arrangement of points that extends indefinitely in one direction from a point called its endpoint.
3 onvex and oncave Regions: region is convex if for every pair of points in the region, the line segment connecting them is also in the region. region is concave if there is at least one pair of points in the region where the connecting line segment leaves the region. onvex: oncave:
4 ngle: It s the union of two line segments with a common endpoint or the union of two rays with a common endpoint. The common endpoint is called its vertex, and the line segments or rays are called its sides. D E F DEF Interior/Exterior of an ngle: n angle that is formed by two rays divides a plane into three parts: the angle, the interior of the angle, and the exterior of the angle. Exterior(concave) D E Interior(convex) F
5 djacent ngles: They are two angles that share a vertex, have a common side, but whose interiors don t intersect. D D and are adjacent angles. cute ngle: n angle whose degree measure is less than 90. m 90
6 Right ngle: n angle whose degree measure is equal to 90. m 90 Obtuse ngle: n angle whose degree measure is greater than 90 but less than m 180
7 Straight ngle: n angle whose degree measure is equal to 180. Interior and exterior are convex. m 180 Reflex ngle: n angle whose degree measure is greater than 180 but less than 360. Interior is concave, and the exterior is convex. 180 m 360
8 Vertical ngles: When two lines intersect, angles are formed. The pairs of nonadjacent angles are called vertical angles and 3 are vertical angles. 2 and 4 are vertical angles. Vertical angles are congruent.
9 omplementary ngles: If the measures of two angles add up to 90, then the two angles are complementary. D D and D are complementary angles. Supplementary ngles: If the measures of two angles add up to 180, then the two angles are supplementary. D D and D are supplementary angles.
10 Find the value of x.
11 Two Parallel Lines Intersected by a Transversal: orresponding ngles: Pairs of angles that match up. 1 and 5 are corresponding angles. 2 and 6 are corresponding angles. 3 and 7 are corresponding angles. 4 and 8 are corresponding angles. orresponding angles are congruent.
12 lternate Interior ngles: Pairs of non-adjacent angles between the parallel lines but on opposite sides of the transversal. 3 and 5 are alternate interior angles. 4 and 6 are alternate interior angles. lternate interior angles are congruent. omplete the labelling of the angle measures in the following pair of parallel lines cut by a transversal.
13 The sum of the angle measures in a triangle: So m 1 m 2 m 3
14 Find the missing angle measure in the following triangle.
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