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Transcript
Geometry Chapter 1 Study Guide I. Terms A. Line: Through any two points exists exactly one line. Lines have no defined endpoints. B. Collinear: Points on the same line C. Plane: Through any three noncollinear points form exactly one plane. D. Line Segment: A part of a line with two defined endpoints E. Ray: A part of a line with one defined endpoint and an arrowhead describing the direction of the ray. F. Opposite Rays: Form a line G. Midpoint: A point that divides a segment into two congruent segments. H. Segment or Angle Bisector: A point, ray, line, line segment, or plane that intersects a segment or angle at its midpoint. I. Angle Types: 1. Acute Angles are less than 90˚ 2. Obtuse Angles are greater than 90˚ but less than 180˚ 3. Right Angles are equal to 90˚ 4. Straight Angles are equal to 180˚ J. Complementary Angles: Two angles whose sum is 90˚ K. Supplementary Angles: Two angles whose sum is 180˚ L. Adjacent Angles: Two angles that share a common side M. Linear Pair: Two adjacent supplementary angles N. Vertical Angles: Two angles whose sides from opposite rays, vertical angles are congruent to each other O. Polygon: A Figure formed by three or more line segments P. Equilateral Polygon: All sides are congruent Q. Equiangular Polygon: All angles are congruent R. Regular Polygon: Is both Equilateral and Equiangular II. Formulas and Postulates A. Segment Addition Postulate 1. If B is between A and C, then AB + BC = AC 2. If AB + BC = AC, then B is between A and C A B C 3. Examples: a. Find XZ X 23 Y 50 Z b. Find GH F 37 144 G H c. Find AB 36 A -2x + 12 B 4x + 20 B. Angle Addition Postulate (Same as Segment Addition Postulate above) C. Midpoint Formula 1. 𝑋1+𝑋2 2 ( , 𝑌1+𝑌2 ) 2 2. Example 1: Given: M is a midpoint of RS, R (1,-3) and S (4,2) Find midpoint M C 3. Example 2: Given: M (8,12) is a midpoint of LP, L(-4, 2) Find endpoint P D. Distance Formula 1. 𝐷 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)² 2. Example: Find the distance between R (1,-3) and S (4,2) E. Perimeter (distance around) and Area (space inside) Formulas Perimeter (ft) Area (ft)2 P = 2l + 2w A=l∙w Square P = 4s A = s² Triangle P=b+h+s Shape Rectangle Circle Circumference = 2𝜋𝑟 𝑜𝑟 𝑑𝜋 1 A = 2 b∙h or A = 𝜋𝑟 2 𝑏 ∙ℎ 2