Constructions 1: Perpendicular and Angle Bisectors

This lesson introduces fundamental geometric construction techniques using a compass and ruler. Students will learn how to construct perpendicular bisectors of lines and angle bisectors.

Definition: A perpendicular bisector cuts a line in half at right angles.

The lesson begins with a review of key terms:

Vocabulary:

• Perpendicular: Lines that intersect at a right (90 degree) angle
• Intersect: To cross over or have a common point
• Arc: Any smooth curve joining two points

A step-by-step worked example demonstrates how to construct a perpendicular bisector of a line:

1. Draw a line of given length
2. Open compass to more than half the line's length
3. Draw arcs from each endpoint
4. Connect intersection points of arcs

Highlight: Construction marks should not be erased, as they are part of the solution.

Construction Practice and Applications

This section provides a set of practice exercises for students to apply their newly learned construction skills.

Task 1 (15 minutes):

1. Draw an 8cm line and construct its perpendicular bisector
2. Draw a 6cm line and construct its perpendicular bisector
3. Draw and construct angle bisectors for the following angles: a) 60° b) 40° c) 90° d) 110° e) 150° f) 54° g) 220°

Highlight: These exercises cover a range of angle measures, helping students become proficient in constructing angle bisectors using a compass for various scenarios.

The remaining pages of the document provide space for students to complete these construction exercises, emphasizing the importance of showing all construction arcs and lines clearly.

Example: When bisecting a 90° angle, students should draw the initial angle, then use their compass to create intersecting arcs that determine the bisector line.

By practicing these constructions, students develop a strong foundation in geometric reasoning and precise drawing techniques essential for more advanced geometry topics.