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Foundations for Geometry Chapter 1

Foundations for Geometry Chapter 1. By: Peter Spencer Maria Viscomi Ian McGreal. 1.1 Understanding Points, Lines, and Planes. Undefined Term-can not be defined by using figures Point- names a location and has no size, it is represented by a dot; named with a capital letter

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Foundations for Geometry Chapter 1

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  1. Foundations for Geometry Chapter 1 By: Peter Spencer Maria Viscomi Ian McGreal

  2. 1.1 Understanding Points, Lines, and Planes • Undefined Term-can not be defined by using figures • Point- names a location and has no size, it is represented by a dot; named with a capital letter • Line- is a straight path that has no thickness and extends forever; named with a lowercase letter or two points on the line • Plane-a flat surface that has no thickness and extends forever; named by a script capital letter or three points not on a line • Collinear- points on the same line • Coplanar- points on the same plane

  3. 1.1 Continued • Segment (or line segment)- the part of a line consisting of two points and all the points between them; named by its two endpoints • Endpoint- point at the end of a segment or the starting point of a ray; named by a capital letter • Ray- part of a line that starts at an endpoint and extends forever in one direction; named by its endpoint and any other point on the ray • Opposite Rays- two rays that have a common endpoint and form a line; named by common endpoint and any other point on each ray • Postulate- a statement that is accepted as true without proof

  4. 1.2 Measuring and Constructing Segments • Coordinate- a number used to identify the location of a point • Distance- absolute value of the difference of the coordinates • Length- distance between two points • Congruent Segments- segments that have the same length • Construction- way of creating a figure that is more precise • Between- a point in between two points is between them • Midpoint- point that bisects • Bisects- divides a segment into two congruent segments • Segment bisector- any ray, segment, or line that intersects a line at the midpoint

  5. 1.3 Measuring and Constructing Angles • Angle- figure formed by two rays, or sides, with a common endpoint • Vertex- the common endpoint in an angle • Interior of an angle-the set of all points between the sides of an angle • Exterior of an angle- the set of all points outside the angle • Degree- 1/360th of a circle; what angles are measured in

  6. 1.3 Measuring and Constructing Angles • Acute Angle- an angle measured greater than 0 but less than 90 • Obtuse Angle- an angle measured greater than 90 but less than 180 • Right Angle- an angle measured 90 • Straight Angle- an angle measured 180 • Congruent Angles- angles with the same measure • Angle Bisector-a ray that divides and angle into two congruent angles

  7. 1.4 Pairs of Angles • Adjacent angles- two angles in the same plane with a common vertex and a common side, but no common interior points • Linear pair- pair of adjacent angles whose non-common sides are opposite rays • Complementary angles- two angles whose measures have a sum of 90 • Supplementary angles- two angles whose measures have a sum of 180 • Vertical angles- two nonadjacent angles formed by two intersecting lines

  8. 1.5 Using Formulas in Geometry • Perimeter- sum of the side lengths of the figure • Area- number of non-overlapping square units of a given size that exactly cover the figure • Base- any side of a triangle • Height- segment from a vertex that forms a right angle with a line containing the base • Diameter- a segment that passes through the center of a circle and whose endpoints are on the circle • Radius- a segment whose endpoints are the center of the circle and a point on the circle • Circumference- distance around a circle • Pi- an irrational number; 3.14159265…..

  9. 1.6 Midpoint and Distance in the Coordinate Plane • Coordinate plane- a plane that is divided into four regions by a horizontal and a vertical line • Leg- two sides that form the right angle of a right triangle • Hypotenuse- the side across from the right angle that stretches from one leg to the other

  10. 1.7 Transformations In the Coordinate Plane • Transformation- change in the position, size, or shape of a figure • Preimage- the original figure before transformation • Image- the figure after transformation • Reflection- (flip) a transformation across a line • Rotation- (turn) transformation about a point • Translation- (slide) transformation in which all points move the same distance and direction

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