Answer to Question #124093 in Geometry for Tina

Question

Discuss how you will teach a Grade 9 class how to construct angle 45° without using
a protractor. In your discussion, include the steps that you will follow and all
mathematical instruments that you will use.

Answer 1

Mathematical Instruments used:

1)Scale

2)Compass

STEPS OF Construction:

1)Draw a line segment , with a scale.

2)With compass open more than half of length  and the pointer of compass at “A” draw arcs on top and bottom of line

3)With same radius of compass, with pointer at “B” draw arcs on top and bottom of line AB.

4)Join the intersection of these arcs at points C & D, this gives the perpendicular bisector of  . Since    . Therefore ∠ BOC is 90°.

5)Now draw angle bisector of ∠ BOC ; open radius of compass more than half of the line OB, draw arcs on lines  & , with compass pointed at “O”

6)Draw arcs from points “E” and “F” where arcs cut the lines  and  respectively.

7)Let point of intersection of these arcs be “G”

8)Join “O” and “G”

9)Since  is bisector of ∠ BOC (=90°)

∠ BOG = 45° Ans.