5.3: Triangle Sides & Angles
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
Use this document to record your answers.
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).
\begin{align*}\angle{A}\end{align*} | \begin{align*}\angle{B}\end{align*} | \begin{align*}\angle{C}\end{align*} |
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11. Can a triangle have three acute angles?
Make a sketch to support your answer.
12. Can a triangle have three right angles?
Make a sketch to support your answer.
13. Can a triangle have three obtuse angles?
Make a sketch to support your answer.
14. Look back at your answers for Exercises 8 and 9.
Can you explain why you got these answers?