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Shop Essentials (Applied Mathematics)

Geometry: Triangles 161

The class Geometry: Triangles discusses triangles and the specific mathematical operations unique to them. While the triangle is a very basic shape, it can be found as a part of more complex shapes. Triangles are often used as the basic shapes that compose three-dimensional CAD designs. Right triangles also form the basis of trigonometry. Since triangles are so commonly used, an understanding of the types of triangles and the methods for calculating missing information from them is essential to users.

After taking this class, users will be able to categorize triangles by their sides and angles, calculate missing angles based on the measurements of other angles, and determine the area of a triangle.

  • Difficulty Beginner

  • Format Online

  • Number of Lessons 18

  • Language English

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Course Outline
  • What Is a Triangle?
  • Interior Angles
  • Lines and Angles
  • Sum of Interior Angles: Sample Problem
  • Basic Properties of Triangles Review
  • Constructing a Triangle: Sample Problem
  • Types of Triangles by Sides
  • Types of Triangles by Angles
  • Isosceles and Equilateral Triangles
  • Triangle Categorization
  • The Relationship Between Sides and Angles
  • Calculating Area of a Triangle
  • Triangle Calculations Review
  • Right Triangles
  • Right Triangle: Sample Problem
  • Two Right Triangles: Solving for Angles
  • Two Right Triangles: Second Solution
  • Right Triangle Review
Objectives
  • Define triangle.
  • Describe the interior angles in a triangle.
  • Describe the properties of lines and adjacent and vertical angles.
  • Calculate a missing angle from a triangle.
  • Calculate a missing angle by constructing a triangle.
  • Identify the different types of triangles by their sides.
  • Identify the different types of triangles by their angles.
  • Distinguish between isosceles and equilateral triangles.
  • Describe the relationship between sides and angles in triangles.
  • Calculate the area of a triangle.
  • Describe the properties of right triangles.
  • Solve for the missing measurements in right triangles.
  • Solve for missing angles in two right triangles.
  • Solve for missing angles in two right triangles.
Glossary
Vocabulary Term
Definition

acute triangle

A triangle containing three angles that each measure less than 90 degrees. All three angles must add up to 180 degrees.

adjacent angles

Two angles that share the same vertex and one side. Adjacent angles do not overlap.

altitude

Altitude is the line drawn perpendicular to the base that represents the height of a form. In a triangle, this line is drawn from the base to the opposite vertex.

area

A measurement of the amount of space contained within a flat, enclosed shape. The area of a triangle is calculated as one half the base times the altitude (1/2 × b × a).

base

The side of a triangle from which the height is constructed. In an isosceles triangle, the base is the side that is not equal to the other sides.

base

The side of a triangle from which the height is constructed. The base is the one side that is not equal to the other sides in an isosceles triangle.

base angles

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

congruent

Equal or similar to each other. In an equilateral triangle, all sides are congruent to each other.

equilateral triangle

A triangle with three equal sides that are the same length. Since all three sides of an equilateral triangle are the same length, all three angles must be equal.

interior angles

An angle located within a closed figure. A triangle has three interior angles.

intersecting lines

Lines that meet, cut across, or overlap. Two intersecting lines form the shape of an 'X' and create vertical angles.

isosceles triangle

A triangle that has two equal sides. An isosceles triangle also contains two equal angles.

legs

The two sides that are equal in length in an isosceles triangle. Since the legs of an isosceles triangle are equal in length, the angles opposite them must also be equal.

line

A series of points that extends endlessly in two directions. A line measures 180 degrees.

obtuse triangle

A triangle containing one angle that is greater than 90 degrees. The other two angles must total less than 90 degrees.

perpendicular

A line that forms an angle of 90° with another line. The altitude of a triangle is perpendicular to the base.

pocket

An interior recess that is cut into the surface of a workpiece. Pockets may be round or rectangular.

right triangle

A triangle containing exactly one 90 degree angle. The other two angles must total exactly 90 degrees.

scalene triangle

A triangle with three unequal sides. The angle opposite the longest side is the largest angle.

sum

The resulting amount from combining or adding numbers together. The sum of interior angles of triangles is always 180 degrees.

triangle

A closed figure with exactly three sides. The three sides meet to form three interior angles.

vertex

A point where two lines or line segments meet or intersect. A triangle has three vertices.

vertex angle

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

vertical angles

Two angles that share the same vertex and are positioned directly opposite one another. Vertical angles have the same values and are formed whenever two lines intersect.