In this lesson, students learn two constructions:

• a line perpendicular to a given line through a point on the line
• an angle bisector

For the perpendicular line construction, students rely on their experience with the perpendicular bisector construction. The angle bisector construction is then connected to the perpendicular line construction with the observation that constructing a perpendicular line is the same as bisecting a straight angle. An angle bisector is a line through the vertex of an angle that divides it into two equal angles. Students make use of structure when they decide how to apply what they already know about constructions to construct perpendicular lines and angle bisectors (MP7). Students are likely to struggle to come up with a construction technique. This is an opportunity to encourage them to persevere in solving problems (MP1).

If students have ready access to digital materials in class, they can choose to perform all construction activities with the GeoGebra Constructions Tool accessible in the Math Tools or available at https://im612.org/construction-tool. 

Math Community

In this lesson, students review the themes that arose when they shared their initial thoughts in Exercise 1 about what they think it should look like and sound like to do math together as a community. Students then have a chance to both affirm and add to the ideas that were generated.