<< Chapter < Page Chapter >> Page >
By the end of this section, you will be able to:
  • Solve applications using properties of triangles
  • Use the Pythagorean Theorem
  • Solve applications using rectangle properties

Before you get started, take this readiness quiz.

  1. Simplify: 1 2 ( 6 h ) .
    If you missed this problem, review [link] .
  2. The length of a rectangle is three less than the width. Let w represent the width. Write an expression for the length of the rectangle.
    If you missed this problem, review [link] .
  3. Solve: A = 1 2 b h for b when A = 260 and h = 52 .
    If you missed this problem, review [link] .
  4. Simplify: 144 .
    If you missed this problem, review [link] .

Solve applications using properties of triangles

In this section we will use some common geometry formulas. We will adapt our problem-solving strategy so that we can solve geometry applications. The geometry formula will name the variables and give us the equation to solve. In addition, since these applications will all involve shapes of some sort, most people find it helpful to draw a figure and label it with the given information. We will include this in the first step of the problem solving strategy for geometry applications.

Solve geometry applications.

  1. Read the problem and make sure all the words and ideas are understood. Draw the figure and label it with the given information.
  2. Identify what we are looking for.
  3. Label what we are looking for by choosing a variable to represent it.
  4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
  5. Solve the equation using good algebra techniques.
  6. Check the answer by substituting it back into the equation solved in step 5 and by making sure it makes sense in the context of the problem.
  7. Answer the question with a complete sentence.

We will start geometry applications by looking at the properties of triangles. Let’s review some basic facts about triangles. Triangles have three sides and three interior angles. Usually each side is labeled with a lowercase letter to match the uppercase letter of the opposite vertex.

The plural of the word vertex is vertices . All triangles have three vertices . Triangles are named by their vertices: The triangle in [link] is called A B C .

A triangle with vertices A, B, and C. The sides opposite these vertices are marked a, b, and c, respectively.
Triangle ABC has vertices A, B, and C. The lengths of the sides are a, b, and c.

The three angles of a triangle are related in a special way. The sum of their measures is 180 ° . Note that we read m A as “the measure of angle A.” So in A B C in [link] ,

m A + m B + m C = 180 °

Because the perimeter of a figure is the length of its boundary, the perimeter of A B C is the sum of the lengths of its three sides.

P = a + b + c

To find the area of a triangle, we need to know its base and height. The height is a line that connects the base to the opposite vertex and makes a 90 ° angle with the base. We will draw A B C again, and now show the height, h . See [link] .

A triangle with vertices A, B, and C. The sides opposite these vertices are marked a, b, and c, respectively. The side b is parallel to the bottom of the page, and it has a dashed line drawn from vertex B to it. This line is marked h and makes a right angle with side b.
The formula for the area of A B C is A = 1 2 b h , where b is the base and h is the height.

Triangle properties

A triangle with vertices A, B, and C. The sides opposite these vertices are marked a, b, and c, respectively. The side b is parallel to the bottom of the page, and it has a dashed line drawn from vertex B to it. This line is marked h and makes a right angle with side b.

For A B C

Angle measures:

m A + m B + m C = 180
  • The sum of the measures of the angles of a triangle is 180 ° .

Perimeter:

P = a + b + c
  • The perimeter is the sum of the lengths of the sides of the triangle.

Area:

A = 1 2 b h , b = base , h = height
  • The area of a triangle is one-half the base times the height.

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask