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Transcript
Geometry CH 1 Study Guide Name_____________________________ Date__________________ VOCABULARY point collinear points opposite rays midpoint formula segment addition postulate supplementary angles complementary angles angle addition postulate line line segment intersect angle bisector collinear plane distance formula congruent segments adjacent angles plane angle ray sides linear pair vertex acute angle bisect midpoint vertical angle obtuse angle congruent angle right angle straight angle segment bisector 1.2 Points, Lines, Planes Point – represents a location, no size, no thickness .A Line – infinite set of points, no thickness, extends in both directions forever (straight line) m A B C D Name - line m, AB AC CB Plane – Flat surface that extends forever, made up of infinite points and lines Must be 3 points not in a line Plane M, Plane ABC Collinear Points – all points that lie on the same line Collinear Plane – all points that lie on the same plane Line Segment – Consists of 2 endpoints and all the points between them Ray – The ray AB consists of the initial point A and all the points that lie on the same A side of A as point B B Opposite Rays –– 2 rays that share exactly 1 point. If C is between A and B, then CA and CB are opposite rays. A C B Intersect – 2 or more geometric figures intersect if they have 1 or more points in common. Intersecting Planes Line Interesting Plane 2 planes intersect in a line. 1.3 Segments and Their Measures Distance/Length – same meaning AB = line segment AB AB = refers to the length of segment AB AB = line AB AB = ray AB Between refers to collinear points. When 3 points lie on a line, you can say that one of them is between the other two. Distance Formula AB = ( x 2 x1 ) 2 ( y 2 y1 ) 2 Find the length of the segments. (4 1) (3 1) (3) (2) 94 13 2 AB = 2 2 Congruent Segments – segments that have the same length AB DC (is congruent to) D A B C Segment Addition Postulate – If B is between A and C then AB + BC =AC A B C 2 1.4 Angles and Their Measures Angle – 2 different rays that have the same initial point Sides – the rays that make up the angle. AC AB Vertex – the initial point of the angle Name – A CAB BAC 1 Measure = mCAB 40 Congruent angles – angles that have the same measures A point is in the interior of an angle if it is between points that lie on each side of the angle. A point is in the exterior of an angle if it is not on the angle or in its interior. Angle Addition Postulate – If P is in the interior of RST then mRSP mPST mRST Acute angle – an angle with measure between 0 and 90 20 Right angle – an angle with measure equal to 90 Obtuse angle – an angle with measure between 90 and 180 120 Straight angle – an angle with measure equal to 180 Adjacent angles – 2 angles that share a common vertex and side, but have no common interior points LMN and NMO are adjacent angles 1.5 Segment and Angle Bisectors Midpoint – the point that divides segment into two congruent segments. Bisect – to divide into 2 congruent parts Segment bisector – a segment, ray, line, or plane that midpoint intersects a segment at its Midpoint Formula – If A(x ,y ) and B(x ,y ) endpoints of a segment then the midpoint of AB is x1 x2 y1 y 2 , 2 2 Find the coordinates of the midpoint of AB with A(-2,3) and B(5,-2) Angle Bisector – a ray that divides an angle into 2 adjacent angles that are congruent. 1.6 Angle Pair Relationships Vertical Angles – 2 angles whose sides form 2 pairs of opposite rays Linear Pair – 2 adjacent angles whose non common sides are opposite rays Complementary Angles – 2 angles whose measures have the sum 90 Complementary adjacent Complementary nonadjacent Supplementary Angles – 2 angles whose measures have the sum 180 Supplementary adjacent Supplementary nonadjacent 1.7 Introduction to Perimeter, Circumference, and Area Formulas Square P = 4s A s2 Rectangle Length l and width w P = 2l + 2w Triangle Side lengths a, b, and c, base b, and height h P = a+b+c 1 A bh 2 Circle Radius r C 2r or A r 2 C d