# Geometry Activities: Fun With Angle Bisectors

By Keren Perles

Teaching about angle bisectors in geometry class can seem boring to your students, but these activities with angle bisectors can make the process much more fun and engaging. Choose one based on your students' levels and interests.

## Angle Bisector Picture

When planning teaching activities with angle bisectors, it is important to think about the strengths of your class. One basic activity you can use for a class that has several more artistic students involves making pictures using angle bisectors. There are two versions of this activity, and the first is much simpler than the second. Use the first art activity for younger students or students who are struggling, and use the second for artistic students in older grades or more advanced classes.

Divide the class into small groups, and provide each group with a large piece of butcher paper, a protractor, a ruler, a pencil, and some art supplies. Instruct each group to make a large X on the butcher paper by connecting the corners of the paper using two diagonal lines. Point out the four angles that have formed, and tell students to find and draw the angle bisector of each angle. Tell students that this will form additional angles, which will have their own bisectors, and so on. Students should continue finding bisectors until they have a given number of sections. They can then use the art supplies to color in each section for a piece of "angle bisector artwork" that looks a bit like an explosion.

The more advanced version of this activity entails challenging students to draw an actual picture using only straight lines. The picture must follow only two rules: 1) It must be a recognizable picture of an actual object, and 2) Every line in the picture must be either an angle bisector or part of an angle that has a bisector.

## Discovery Learning About Angle Bisectors

Students who are just beginning to learn about angle bisectors may benefit from a hands-on activity to help them learn how angle bisectors affect the rest of the angles in a triangle. To do this activity, divide students into groups and let them loose with protractors, pencils, and the question, "What facts hold true about angle bisectors in all triangles?" If students get stuck, guide them by asking them to draw all three angle bisectors and examine where the three bisectors intersect (this point is called the "incenter" of the triangle).

## Angle Bisectors and Midpoints

Students may find this activity intriguing. Instruct them to use their rulers to draw three lines connecting the midpoints of a triangle's three sides. These three sides should form a smaller triangle within the original triangle. Encourage them to use their protractors to draw in the angle bisectors of the larger triangle's angles, and then to draw in the angle bisectors of the smaller triangle's angles. They may be surprised at what they see. As a class, brainstorm different reasons for why the two triangles always share angle bisectors. Students can work individually or in groups to try to prove their reasoning. (They can also explore this triangle further, if they have learned about congruence.)

These activities with angle bisectors, like other geometry activities, can help students gain more familiarity with the concept and give them plenty of practice with how it works. They can also help stretch students' minds to understand how real mathematicians approach interesting geometric problems.