Shop Essentials (Applied Mathematics)

Shop Geometry Overview 170

This class presents a general overview and refresher for the the most common rules of geometry.

  • Difficulty Beginner

  • Format Online

  • Number of Lessons 20

  • Language English

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Course Outline
  • Objectives
  • What Is Geometry?
  • Points, Lines, and Planes
  • Line Segments, Rays, and Angles
  • Types of Angles
  • Pairs of Angles
  • Parallel and Perpendicular Lines
  • Interior and Exterior Angles
  • Polygons
  • Triangles
  • Triangles Grouped by Their Sides
  • Triangles Grouped by Their Angles
  • Quadrilaterals
  • Parallelograms
  • Rectangles
  • Rhombi and Squares
  • Circles
  • Circles: Secants and Tangents
  • Circles: Circumference and Area
  • Summary
Objectives
  • Define geometry.
  • Describe the basic features that make up geometric shapes.
  • Describe the basic geometric features that can be measured.
  • Identify the different types of angles.
  • Identify the different pairs of angles.
  • Distinguish between perpendicular and parallel lines.
  • Describe the angles that are formed when a line intersects parallel lines.
  • Describe the characteristics of a polygon.
  • Describe the characteristics of a triangle.
  • Match the type of triangle with the characteristics of its sides.
  • Match the type of triangle with the characteristics of its angles.
  • Describe the characteristics of a quadrilateral.
  • Describe the characteristics of a parallelogram.
  • Describe the characteristics of a rectangle.
  • Describe the characteristics of a rhombus.
  • Describe the characteristics of a square.
  • Identify the parts of a circle.
  • Distinguish between a secant and a tangent.
  • Distinguish between circumference and area.
Glossary
vocabulary term
Definition

acute angle

An angle that measures more than 0° but less than 90°.

adjacent angles

Two angles in the same plane that share a common side and common vertex.

area

The amount of space, or number of square units, inside a closed figure.

base

The side of a triangle from which the height is constructed.

base angle

The angle that is formed by the base and one leg in an isosceles triangle. The base angles are always equal.

chord

A line segment that divides a circle into two segments.

circle

A geometric shape formed by the group of points that are an equal distance from a point, or center.

circumference

The boundary or perimeter around a circle. Circumference measures the distance around a circle.

complementary angles

Two angles whose measurements add up to 90°.

consecutive angles

Angles that occur one right after the other. Consecutive angles are on either end of the same line segment in a polygon.

consecutive sides

Two sides that occur one right after another and that share an endpoint. Consecutive sides connect to form a closed figure in a polygon.

degree

The most commonly used unit of measurement for an angle. The degree symbol is a small circle above and to the right of a number, as in 90°.

diameter

The distance from one edge of the circle to the opposite edge that passes through the center.

endpoint

One of two points on a line segment that signifies where the line segment ends.

equiangular

Having angles that are all equal.

equidistant

Of the same, or equal distance.

equilateral triangle

A triangle with three equal sides and three equal angles.

exterior angle

An angle that lies outside a closed figure or outside parallel lines.

geometry

A section of mathematics that involves the measurements, properties, and relationships of all shapes and sizes of things.

height

A perpendicular line drawn from the highest point in the triangle to the base on the opposite side.

interior angle

An angle that lies inside a closed figure or between parallel lines.

isosceles triangle

A triangle with two equal sides.

leg

One of the two equal sides in an isosceles triangle.

line

A set of numerous points that extend endlessly in two directions. A line is the quickest way to get from one point to another.

line segment

A portion of a line that has a beginning and an end. A line segment can be measured.

major segment

The larger portion of a circle that is cut off by a chord.

minor segment

The smaller portion of a circle that is cut off by a chord.

obtuse angle

An angle that measures more than 90° but less than 180°.

opposite sides

The sides in a quadrilateral that occur opposite from one another.

parallel lines

Lines that do not intersect and do not share any points. Parallel lines are equally distant from each other.

parallelogram

A quadrilateral with opposite parallel sides.

perpendicular lines

The formation of a right angle between two lines. The corner of a piece of paper is formed by perpendicular lines.

pi

A special constant value that relates the diameter of a circle to its circumference. Pi is used to find the circumference and area of a circle and applies for any circle.

plane

A flat surface that extends infinitely in any direction in three dimensions. A plane is represented by a closed four-sided figure.

point

A dot that indicates a definite position or location. A point has no width, depth, or length.

point of tangency

The point at which a tangent touches a circle.

polygon

A closed shape consisting of line segments that has at least three sides. Triangles, quadrilaterals, rectangles, and squares are all types of polygons.

protractor

A tool that can be used to measure or create an angle.

quadrilateral

A polygon with four sides.

radii

The plural term for radius.

radius

The distance from the center to the edge of a circle.

ray

A portion of a line that has only one endpoint and extends infinitely in one direction. The length of a ray cannot be measured.

rectangle

A parallelogram with four right angles.

regular polygon

A type of polygon with sides and angles that are all equal. A stop sign is a regular polygon with eight sides and eight angles.

rhombi

The plural term for rhombus.

rhombus

A parallelogram with equal sides. A rhombus often resembles a diamond.

right angle

An angle formed by two lines that are perpendicular to one another and measures exactly 90°. The corner of a piece of paper is a right angle.

scalene triangle

A triangle with three unequal sides.

secant

A line, line segment, or ray that intersects a circle at two points.

square

A rectangle with four equal sides.

straight angle

An angle that measures 180°. A straight angle resembles a straight line.

supplementary angles

Two angles whose measurements add up to 180°.

tangent

A line, line segment, or ray that touches a circle at exactly one point.

transversal line

A line that crosses two or more lines at different points.

triangle

A polygon with three sides.

vertex

The point where the two sides of an angle intersect.

vertex angle

The angle formed by the two equal legs in an isosceles triangle. The vertex angle is opposite from the base.

vertical angles

Two angles positioned across from each other in the same plane but not next to each other. Vertical angles are formed by intersecting lines and they share the same vertex.

vertices

The plural term for vertex.