Concept Byte: Paper Folding Bisectors

Use With Lesson 5-3

ACTIVITY

In Activity 1, you will use paper folding to investigate the bisectors of the angles of a triangle.

Activity 1

• Step 1 Draw and cut out three different triangles: one acute, one right, and one obtuse.
• Step 2 Use paper folding to make the angle bisectors of each angle of your acute triangle. What do you notice about the angle bisectors?
• Step 3 Repeat Step 2 with your right triangle and your obtuse triangle. Does your discovery from Step 2 still hold true?

Folding an angle bisector

In Activity 2, you will use paper folding to investigate the perpendicular bisectors of the sides of a triangle.

Activity 2

• Step 1 Draw and cut out two different triangles: one acute and one right.
• Step 2 Use paper folding to make the perpendicular bisector of each side of your acute triangle. What do you notice about the perpendicular bisectors?
• Step 3 Repeat Step 1 with your right triangle. Does your discovery from Step 2 still hold true?

Folding a perpendicular bisector

Exercises

1. Make a Conjecture Make a conjecture about the bisectors of the angles of a triangle.
2. Make a Conjecture Make a conjecture about the perpendicular bisectors of the sides of a triangle.
3. Extend Draw and cut out an obtuse triangle. Fold the perpendicular bisectors.
   1. How do the results for your obtuse triangle compare to the results for your acute and right triangles from Activity 2?
   2. Based on your answer to part (a), how would you revise your conjecture in Exercise 2?
4. Extend For what type of triangle would the three perpendicular bisectors and the three angle bisectors intersect at the same point?

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