Tues 11th Jun - Mathematical Constructions

LEARNING OBJECTVIE: To understand how to accurately construct a line bisector, an angle bisector ...without using a measuring device.

SUCCESS CRITERIA: You will be able to use a pencil, ruler and pair oc compasses to construct a variety of constructions

ENGAGEMENT ACTIVITY: Why We Learn about Constructions

LESSON: Discuss above article and then look at setting up and using a pair of compasses accurately.

Then show and practice the following constructions

Perpendicular bisector of a line segment

Bisecting an angle

Extension: Choose other constructions from this List

Copy a line segment

Perpendicular bisector of a line segment

Perpendicular from a line at a point

Perpendicular from a line through a point

Perpendicular from endpoint of a ray

Divide a segment into n equal parts

Parallel line through a point (angle copy method)

Parallel line through a point (rhombus method)

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Polygons

• Hexagongiven one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object