Exercise 29 Page 73

Practice makes perfect

a Let's first sketch ∠ B on paper.

To construct a congruent angle to ∠ B, we draw a ray underneath it like below.

Next, we will have to use a compass. Open up the compass and draw two identical arcs from the vertex of each angle.

Next, change the compass settings and measure the size of ∠ B.

Using that same compass settings, we can measure the same angle on our copy.

Finally, to copy the angle, we will draw a second ray from B' and through the intersection of the two lines.

b An angle can be bisected using a compass.

Start by placing the sharp end of the compass at the vertex of the angle. Draw an arc across the rays.

Next, place the sharp end of the compass at the point where one ray intersects the arc. Draw a new arc.

Using the same compass settings, do the same with the other ray, making sure this arc intersects the previous arc.

Finally, we will use a ruler or a straightedge to draw a ray from the vertex through the intersection between the two arcs.

This ray is the angle bisector, and divides the angle into two angles of equal measure.

Exercises p.70-74

Hints