Chapter 1

Chapter 1

1. 1.1

   • Point
     • Basic building block of geometry
     • Has no length, width or depth
     • One of the undefined terms of geometry
   • Line
     • Straight, continous arrangement of infinitely many points
     • Has length, but no width or depth
     • Created by two points
     • One of the undefined terms of geometry
   • Plane
     • Has length and width, but no depth
     • Needs 3 noncollinear points
   • Co-
     • Collinear - (points) on the same line
     • Coplanar - (points) on the same plane
   • Line segment
     • Consists of 2 points callled endpoints
     • Made up of all of the collinear points in between the endpoints
   • Congruent
     • Same/equal measure or length
   • Midpoint
     • point on a line segment that is the same distance from both endpoints
   • Ray
     • The part of a line that consists of a point and all the points after that point on one side of the line

2. 1.2

   • Angle
     • formed by 2 rays that share a common endpoint, provided that the 2 rays are noncollinear
     • Vertex
       • common endpoint of the 2 endpoints
     • Sides
       • 2 rays of the angle
   • Measure of an Angle
     • smallest amount of rotation about the vertex form one ray to the other
     • Reflex Measure of an Angle
       • the largest amount of rotation less that 360° between the 2 rays
   • Protractor
     • Tool used to measure angles
   • Congruent
     • Same or equal measure
   • Angle Bisector
     • A ray is the angle bisector if it contains the vertex and divides the angle into 2 congruent angles.

3. 1.3

   • Parallel Lines
     • 2 coplanar lines that never intersect
     • 2 noncoplanar lines that never intersect are called skew lines
   • Perpendicular Lines
     • two coplanar lines that intersect at a right angle
   • Angles
     • Right Angle
       • a 90° angle
     • Acute Angle
       • an angle less than 90°
     • Obtuse Angle
       • an angle more than 90° but less than 180°
     • Complimentary Angles
       • 2 angles that add to 90°
     • Supplementary Angles
       • 2 angles that add to 180°
   • Vertical Angles
     • angles formed by 2 intersecting lines that share a common vertex but not a common side
   • Linear Pair of Angles
     • 2 angles that share a vertex and a common side and their noncommon sides form a line

4. 1.4

   • • Concave Polygon - at least one diagonal is outside the polygon
     • Convex Polygon - all diagonals are inside the polygon
     • Congruent Polygons - Corresponding angles and sides are congruent
     • Perimeter - The sum of lengths of a polygon's side
     • Regular Polygon - All sides and angles are equal
       • Equilateral Polygon - All sides are equal
       • Equiangular Polygon - All angles are equal

5. 1.5

   • Triangles!
     • Right Triangle - a triangle with one (and only one) right angle
     • Acute Triangle - a triangle with all acute angles
     • Obtuse Triangle - A triangle with one obtuse angle
     • Scalene Triangle - No sides have equal lengths
     • Isosceles Triangle - At least 2 congruent sides
     • Equilateral Triangle - 3 congruent sides

6. 1.6

   • Quadrilaterals!
     • Trapezoid - A quadrilateral that exactly 1 set of parallel lines
     • A quadriateral with 2 distinct pairs of consecutive congruent sides
     • Parallelogram - A quadrilateral with 2 pairs of parallel lines
     • Rhombus - An equilateral parallelogram
     • Rectangle - an equiangular parallelogram
     • Square - an equiangular rhombus

7. 1.7

   • Circle - the set of all points in a plane at a given distance from a given point
     • Center - The given point
     • Radius - The given distance
     • Chord - a line segment with endpoints on the circle
       • Diameter - a chord that crosses through the center. The longest possible chord
     • Tangent - a line that intersects a circle once
       • Point of Tangeancy - point where the tangent line touches the circle
     • Congruent Circles - 2 or more circles that have the same radius
     • Concentric Circles - 2 or more coplanar cirlces that have the same center
     • Central Angle - the angle with its vertex at the center of the circle, and sides passing through the endpoints of the arc
       • The measure of a major arc is the same as the reflex measure of the central angle

8. 1.8

   • Space Geometry
     • Sphere - All points in space that are a given distance away from a given point
     • Cylinder - an object in space with 2 circular bases and 1 curved side
     • Cone - An object in space with 1 circular side, 1 curved side and a point at the "top"
     • Prism - an object in space with 2 polygon bases and flat sides
     • Cube - An object in space with 6 congruent faces and all congruent angles
     • Pyramid - The cone of prisms
     • Hemisphere - Semicircle of spheres

Imagens e arquivos do mapa