Lines, Angles, and Triangles: Lesson 5 - Properties and Types of Triangles

Properties and Types of Triangles is the fifth of eight self-paced lessons in the “Lines, Angles, and Triangles” section of KET’s GED^{®} Geometry Professional Development Online Course. This lesson demonstrates the types of triangles students may encounter on the GED^{®} Mathematics Test. It shows how they need to combine basic knowledge of triangles with the ability to solve for an angle when it is unknown.

NOTE: This course was created based on the 2002 GED^{®} math test. The geometry instruction in this course is still valid, however, for up-to-date information about the 2014 GED^{®} math test, please visit KET’s GED^{®} Test Info: Mathematics online course.

On the GED^{®} Mathematics Test, it is likely that students will encounter questions related to the nature of triangles.

Students will need to understand the properties of triangles and recognize the different types of triangles.

Students need to be able to find an unknown angle in a triangle when other angles are provided.

This lesson demonstrates the types of triangles students may encounter on the test. It shows how they need to combine basic knowledge of triangles with the ability to solve for an angle when it is unknown.

Note: On the GED Mathematics Test, students will not be asked to produce answers that require recall of terminology — such as the names of the types of triangles.

2Types of Triangles

Watch both videos for an explanation of a triangle’s sides and angles and for a discussion of isosceles and scalene triangles.

Triangles: Isosceles and Scalene

Video: 1m 42s

Triangles: Sides and Angles

Video: 0m 58s

A triangle is a flat figure with three straight sides and three angles. A triangle is named by three letters at its angles. The triangle on the left is named ∆HKL.

The angles in a triangle are measured in degrees. The symbol for degrees is °. The sum of the angle measures in any triangle is 180°. Below are four types of triangles.

Question Use three letters to name the right triangle and the scalene triangle in the figure below.

Step 1 Look for a right angle. Right angles can be marked with a small square. So, ∠A is a right angle. A triangle that includes ∠A is a right triangle.

The right triangle is ∆ABD.

Step 2 Look for a triangle that has sides of three different lengths. ∆CBD is scalene because its sides are three different lengths: 4.5, 9.5, and 13 units.

The scalene triangle is ∆CBD.

Answer Right triangle: ∆ABD; Scalene triangle: ∆CBD

3Finding Unknown Angles

The sum of the angle measures in any triangle is 180°.

To find an unknown angle in a triangle, use the other two angles. Subtract their sum from 180°.

Question In ∆RST, ∠R measures 75° and ∠S measures 30°.

What is the measure of ∠T?

Step 1 Write an equation using the information from the problem. Recall, the sum of the angles in a triangle is 180°. Let x stand for the unknown ∠T.

75° + 30° + x = 180°

Step 2 Simplify by adding 75° + 30° on the left side.

105°+ x = 180°

Step 3 Isolate x by performing the inverse operation on both sides of the equation. Subtract 105° from both sides.

105° – 105°+ x = 180° –105°

x = 75°

Answer∠T = 75°.

4Sample GED Questions

Directions: There are two questions on this page. Each will appear in the blue rectangle below. Click on Question 1 to see the first question, and then select your answer. Click on Question 2 to see the second question, and select your answer. As you solve these problems, also respond to the questions related to building students’ skills.

How could you help students see the individual triangles in this complex figure and apply what they know about types of triangles to solve these problems?

Lines, Angles, and Triangles: Properties and Types of Triangles Skill Review

Document

Printable Resource

In this lesson you have learned about properties and types of triangles. This review consists of key terms and concepts with which you will need to be familiar. Click the view button on the left to access a review sheet.

Below you will also see a Classroom Connection with suggestions for linking this geometry content with your instruction.

Assign directly to your students using the code or link above, without having them log in. Simply tell your students to go to
www.pbsstudents.org and enter the Assignment Code, or click on the Assignment URL to share the assignment as a link.