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# 5.3: Triangle Sides & Angles

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Geometry, Chapter 4, Lesson 5.

In this activity, you will explore:

• The size and location of sides and angles of a triangle
• Triangles that have two equal sides or two equal angles
• The number of acute, right, and obtuse angles in any one triangle

## Problem 1 – Size and Location of Sides and Angles

1. Where is the largest angle of the triangle located relative to the largest side?

2. Where is the smallest angle of the triangle located relative to the smallest side?

Apply The Math

List the angles in order from smallest to largest.

3.

4.

List the sides in order from shortest to longest.

5.

6.

## Problem 2 – The Isosceles Triangle Theorem

7. Make a sketch of your triangle with the side lengths and angle measures labeled.

8. Complete this statement:

If two sides of a triangle are congruent, then _____________________.

9. Complete this statement:

If two angles of a triangle are congruent, then _____________________.

## Problem 3 – Types of Angles in a Triangle

10. Drag a vertex of the triangle and classify the types of angles that exist (acute, right, obtuse).

A\begin{align*}\angle{A}\end{align*} B\begin{align*}\angle{B}\end{align*} C\begin{align*}\angle{C}\end{align*}

11. Can a triangle have three acute angles?

12. Can a triangle have three right angles?

13. Can a triangle have three obtuse angles?

Can you explain why you got these answers?

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