Geometry 1-1. Non-collinear Points not on the same line. Need at least 3 points to be non-collinear since two points are always collinear

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1 Name Geometry 1-1 Undefined terms terms which cannot be defined only described. Point, line, plane Point a location in space Line a series of points that extends indefinitely in opposite directions. It is straight Collinear points on the same line. Two points are always collinear Non-collinear Points not on the same line. Need at least 3 points to be non-collinear since two points are always collinear Plane a flat surface that contains points and lines and it extends indefinitely in all directions Coplanar points on the same plane. Three non-collinear points are always coplanar. Non-coplanar points not on the same plane. Need at least 4 points since 3 points are always coplanar Point Line Plane Model P l A B M A C B M Drawn A dot with a capital block letter next to it. A straight line with arrowheads at both ends. A tilted rectangle Named by One capital block letter One lowercase italic letter or capital block letters for names of two points on the line. One capital script letter or 3 capital block letters for 3 noncollinear points on the plane Facts No size or shape No width or thickness Extends indefinitely in opposite directions Flat surface that contains points and lines and it extends indefinitely in all directions Words/ Symbols Point P P Line l AB, BA Plane M Plane ABC, Plane BAC, Plane CAB, Plane ACB, Plane BCA, Plane CBA

2 Geometry 1- Name Line segment (segment) Part of a line bounded by points, called endpoints A B Segment measure The length of a segment in units a positive number AB or BA Read segment AB or BA AB = BA Read the measure of AB or BA Betweeness of points Point M is between points A and B, 4 5 iff (if and only if) 1. A, B and M are collinear, and A M B. AM + MB = AB 9 4 B Congruent segments Segments are congruent, iff their measurements are equal. X 4 means congruent A D Y If AB XY then AB = XY, and If AB = XY then Congruence also AB XY shown with slashes DE DF Note: Segments are congruent, measures are equal. E F

3 Name Geometry 1-3 Distance formulas P Q Distance between two points on number line a b PQ a b - 6 PQ Distance between two points on the coordinate plane d ( x y 1 x) ( y1 ) A (, 4) B (-1, -1) AB AB AB 34 ( ( 1)) (4 ( 3 5 1)) Midpoint of a segment Point on a segment equidistant from the endpoints A M B M is midpoint of AB, iff AM = MB Midpoint formulas P Q Midpoint of a segment on a number line a b a b Midpoint = if a is at -8 and b is at, midpoint is at -3 Midpoint of a segment on the coordinate plane A (1,)and B (3,-4) Midpoint = x x y, 1 1 y AB Midpoint 1 3 ( 4) ', 1 Segment bisector A line, segment or plane that intersects a segment at its midpoint C A M B If M is midpoint of AB, MC is segment bisector or simply bisector of AB

4 Geometry 1-4 Name Ray Part of a line that starts at an endpoint and continues A B in one direction indefinitely. To name a ray you need points The first is always the endpoint. AB read Ray AB Opposite rays Two collinear rays emanating from the same Endpoint to form a line. The endpoint is the only X Y Z point in common. YX and YZ are opposite rays and form XZ Angle two non-collinear rays emanting from the same endpoint To name an angle (1) one letter A (only when there is one angle at A) () three letters, vertex in middle BAC, CAB when there is more than one angle B (3) or a number placed in the vertex, 1 A 1 C Sides of an angle The rays that form the angle AB and AC Vertex of an angle The common endpoint of the rays, Point A An angle divides a plane into three distinct parts 1. On the angle A, B, C, D, and E B. Interior F, G, and H 3. Exterior I, J, and K A C

5 Angle measurement Every angle is associated with a number greater than 0 and less than 180. The angle measurement unit is in degrees. The symbol for measure of an angle is m Protractor Instrument used to measure angles Classifying angle Right angle Angle whose measure is 90º The symbol placed in an angle indicates a right angle Acute Angle Angle whose measure is greater than 0º and less than 90º 45º Obtuse Angle Angle whose measure is 150º greater than 90º and less than 180º Congruent angles Two angles with the same measure If If A B, then m A mb and m A mb, then A B If the angles are marked with the same number of D E arcs, they are congruent B C Angle bisector A ray that separates an angle into two congruent angles. If BDC CDE, then DC is an angle bisector If DC is an angle bisector, then BDC CDE

6 Geometry 1-5 Name Adjacent angles Two coplanar angles that have (1) same vertex 1 () common side (3) no interior points in common 1 and are adjacent angles Vertical angles Two non adjacent angles formed by the intersection of two lines Vertical angles are congruent 4 3 and 4 are vertical angles and 6 are vertical angles 5 6 Linear pair Two adjacent angles whose non-common sides are opposite rays. 7 and 8 are a linear pair 7 8 Complementary angles Two angles whose measures total 90º 40 º B 50 º A and B are complementary m A mb 90 A Supplementary angles Two angles whose measures total 180º 140 º D 40 º C and D are supplementary C m C md 180 n Perpendicular lines Two lines that intersect m 90º and form a right angle to show perpendicular lines -- m n The symbol placed in an angle indicates a right angle

7 Angle Addition Postulate If D lies in the interior of ABC, then the m ABD mdbc mabc A D B C From diagrams the things we can and cannot assume Things we can assume E 1. All points are coplanar D F A, B and C are collinear 3. BD, BE, and BF intersect AC at B 4. Point D is in the interior of ABE 5. ABD and DBE are adjacent 6. ABD and DBC are a linear pair A B C Things we CANNOT assume 1. EBC. BE BC 3. EBF and FBC is a right angle are complementary 4. B is the midpoint of AC 5. BF BC 6. BD bisects ABE 7. ABD DBE

8 Geometry 1-6 Name Polygon Examples Non-examples Parts of a polygon Sides Vertices Diagonals Convex polygons Concave polygons Regular polygon Classifying a polygon by the number of sides n

9 Perimeter Circumference Area Triangle Square Rectangle Circle Perimeter/ Circumference Area Perimeter = P = Area = A =

10 Geometry 1-7 Name Polyhedron Face Edges Vertex Regular Polyhedron Prism Regular Prism Vertices Faces Edges

11 Pyramid Cylinder Cone Sphere

12 Surface area (T) Volume (V) Surface Area Prism Pyramid Cylinder Cone Volume P = Perimeter of the base T = Total surface area l = slant height B = Area of Base h = height of solid r = radius

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