Triangle Sum Theorem Discovery
- Chris Kucewicz
Part I: Exploration
Experiment with different angle measures by adjusting the location of ONE of the vertices of the given triangle. As you adjust the vertex, consider the following questions:
- Can you make 2 angles greater by moving only 1 vertex?
- Is there a limit for how large a single angle can get?
- What is the least an angle can be?
Part II: Proof
Do NOT move on to Part II until the teacher instructs you to move on (We will proceed to prove the conjecture proposed in Part I. I will use the arrows at the bottom of the following image to scaffold the constructions. The hope is that students will be able to identify the alt. int. angles after parallel lines have been constructed and use knowledge of measure of straight angles in order to understand why the interior angles of any triangle add up to 180 degrees)
What does the Triangle Sum Theorem say? (Students write the triangle sum theorem for reinforcement)
Part III: Application
Find the missing angle (Independent practice. Students apply the Triangle Sum Theorem in order to find missing angles)
Alter the figure and have your shoulder partner find all the missing angles
1) Adjust the vertices to make a different triangles 2) Screen shot the triangle and move imagine to a blank notability note 3) In notability, find the missing angle measure. Show all work. 4) Repeat Steps 1-3, three more times, making a new triangle each time. (You should have 4 different triangles) 5) Submit your notability page to canvas