EDGE Math 8

Inequalities of Two Triangles

Triangle inequalities can also exist between two triangles. Try to investigate this relation by working on the next activity. You will need rubber bands, two sticks connected by a hinge ruler, and a protractor.

Activity

1.	Place a rubber band on the opening of two sticks connected by a hinge. Imagine that the two sticks and the rubber band form a triangle. Name this $ΔCOM .$

2.	Measure $∠ O$ and $\bar{CM} .$

3.	Increase the opening of the hinge to form another triangle. Name it $ΔPAS .$

4.	Measure $∠ A$ and $\bar{PS} .$

5.	Compare the measures of $∠ O$ and $∠ A .$

$m ∠ O_____m ∠ A$

6.	Compare the lengths of $\bar{CM}$ and $\bar{PS} .$

$CM_____PS$

7.	Make a conjecture on how the third sides of two triangles having two congruent sides differ depending on the measures of the opposite angles.

8.	Write the converse of the conjecture you made.

This activity models two theorems on inequalities involving two triangles