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Lesson 1-1

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Lesson 1-1

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  1. Lesson 1-1 Construction Vocabulary Lesson 1-1 Point, Line, Plane

  2. Points • Points do not have actual size. • How to Sketch: Using dots • How to label: Use capital letters Never name two points with the same letter (in the same sketch). A B A C Lesson 1-1 Point, Line, Plane

  3. Lines • Lines extend indefinitely and have no thickness or width. • How to sketch : using arrows at both ends. • How to name: 2 ways (1) small script letter – line n (2) any two points on the line - • Never name a line using three points - n A B C Lesson 1-1 Point, Line, Plane

  4. Collinear Points • Collinear points are points that lie on the same line. (The line does not have to be visible.) • A point lies on the line if the coordinates of the point satisfy the equation of the line. Ex: To find if A (1, 0) is collinear with the points on the line y = -3x + 3. Substitute x = 1 and y = 0 in the equation. 0 = -3 (1) + 3 0 = -3 + 3 0 = 0 The point A satisfies the equation, therefore the point is collinear with the points on the line. A B C Collinear C A B Non collinear Lesson 1-1 Point, Line, Plane

  5. Planes • A plane is a flat surface that extends indefinitely in all directions. • How to sketch: Use a parallelogram (four sided figure) • How to name: 2 ways (1) Capital script letter – Plane M (2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA A M B C Horizontal Plane Vertical Plane Other Lesson 1-1 Point, Line, Plane

  6. Different planes in a figure: A B Plane ABCD Plane EFGH Plane BCGF Plane ADHE Plane ABFE Plane CDHG Etc. D C E F H G Lesson 1-1 Point, Line, Plane

  7. Intersection of Figures The intersection of two figures is the set of points that are common in both figures. The intersection of two lines is a point. m Line m and line n intersect at point P. P n Continued……. Lesson 1-1 Point, Line, Plane

  8. Segment Part of a line that consists of two points called the endpoints and all points between them. Definition: How to sketch: How to name: AB (without a symbol) means the length of the segment or the distance between points A and B. Lesson 1-2: Segments and Rays

  9. Midpoint Definition: A point that divides a segment into two congruent segments Formulas: On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is . In a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and is . Lesson 1-2: Segments and Rays

  10. Bisect Definition: To divide a segment into two congruent parts. Lesson 1-2: Segments and Rays

  11. RA : RA and all points Y such that A is between R and Y. ( the symbol RA is read as “ray RA” ) Ray Definition: How to sketch: How to name: Lesson 1-2: Segments and Rays

  12. Space Definition: a boundless three-dimensional set of all points. Lesson 1-1 Point, Line, Plane

  13. Angle and Points • An Angle is a figure formed by two rays with a common endpoint, called the vertex. ray vertex ray • Angles can have points in the interior, in the exterior or on the angle. A E D B C Points A, B and C are on the angle. D is in the interior and E is in the exterior. B is the vertex. Lesson 1-4: Angles

  14. Naming an angle:(1) Using 3 points (2) Using 1 point (3) Using a number – next slide Using 3 points: vertex must be the middle letter This angle can be named as Using 1 point: using only vertex letter *Use this method is permitted when the vertex point is the vertex of one and only one angle. Since B is the vertex of only this angle, this can also be called . A C B Lesson 1-4: Angles

  15. Naming an Angle - continued Using a number: A number (without a degree symbol) may be used as the label or name of the angle. This number is placed in the interior of the angle near its vertex. The angle to the left can be named as . A B 2 C * The “1 letter” name is unacceptable when … more than one angle has the same vertex point. In this case, use the three letter name or a number if it is present. Lesson 1-4: Angles

  16. Example • K is the vertex of more than one angle. Therefore, there is NO in this diagram. There is Lesson 1-4: Angles

  17. 4 Types of Angles Acute Angle: an angle whose measure is less than 90. Right Angle: an angle whose measure is exactly 90 . Obtuse Angle: an angle whose measure is between 90 and 180. Straight Angle: an angle that is exactly 180 . Lesson 1-4: Angles

  18. Angle Bisector An angle bisector is a ray in the interior of an angle that splits the angle into two congruent angles. Example: Since 4   6, is an angle bisector. 5 3 Lesson 1-4: Angles

  19. Parallel Lines • Parallel lines are coplanar lines that do not intersect. • Arrows are used to indicate lines are parallel. • The symbol used for parallel lines is ||. In the above figure, the arrows show that line AB is parallel to line CD. With symbols we denote, . Lesson 2-3: Pairs of Lines

  20. m n PERPENDICULAR LINES • Perpendicular lines are lines that intersect to form a right angle. • The symbol used for perpendicular lines is  . • 4 right angles are formed. In this figure line m is perpendicular to line n. With symbols we denote, m n Lesson 2-3: Pairs of Lines

  21. Space • Definition: A boundless set of points. Lesson 1-1 Point, Line, Plane

  22. ENDPOINT • Definition: the points located at the ends of a line segment or ray. Both points A and B are endpoints. Point R is an endpoint. Point A is not an endpoint. Lesson 1-1 Point, Line, Plane

  23. CONSTRUCTION • Definition: A precise method of drawing using a pencil, compass, and straightedge. Lesson 1-1 Point, Line, Plane

  24. COMPASS • Definition: a tool used to draw exact circles. Lesson 1-1 Point, Line, Plane

  25. PROTRACTOR • Definition: a tool used to measure the degree of an angle. Lesson 1-1 Point, Line, Plane

  26. STRAIGHT EDGE • Definition: a tool used to draw straight lines. Lesson 1-1 Point, Line, Plane

  27. PERPENDICULAR BISECTOR • Definition: A line, ray or segment that is perpendicular to the segment that it bisects. Lesson 1-1 Point, Line, Plane

  28. Circle Definition Circle : The set of points coplanar points equidistant from a given point. The given point is called the CENTER of the circle. The distance from the center to the circle is called the RADIUS. Center Radius Lesson 8-1: Circle Terminology

  29. B C A O ARCS Arcs : The part or portion on the circle from some point B to C is called an arc. Example: B Semicircle: An arc that is equal to 180°. A C Example: Lesson 8-1: Circle Terminology

  30. Equilateral: A A B C C BC = 3.55 cm B BC = 5.16 cm G H I HI = 3.70 cm Classifying Triangles by Sides Scalene: A triangle in which all 3 sides are different lengths. AC = 3.47 cm AB = 3.47 cm AB = 3.02 cm AC = 3.15 cm Isosceles: A triangle in which at least 2 sides are equal. • A triangle in which all 3 sides are equal. GI = 3.70 cm GH = 3.70 cm Lesson 3-1: Triangle Fundamentals

  31. Classifications of a Polygon Regular: A convex polygon in which all interior angles have the same measure and all sides are the same length Irregular: Two sides (or two interior angles) are not congruent. Lesson 3-4: Polygons

  32. Polygon Names Triangle 3 sides 4 sides Quadrilateral 5 sides Pentagon 6 sides Hexagon 7 sides Heptagon 8 sides Octagon 9 sides Nonagon 10 sides Decagon Dodecagon 12 sides n sides n-gon Lesson 3-4: Polygons