STUDENT NAME: ________________________________________BLOCK # ______________ DATE __________
1. Bisecting a Line Segment
1. Using a ruler, draw on the back of this paper
a line segment similar to the one displayed.
2. Using only a compass and a straight edge,
bisect the line segment you have drawn.
3. Explain how your procedure results in cutting
the line in half.
HINT: To bisect a line segment, the student should: 1) adjust the compass to draw a circle with a radius greater than half the length of the segment and draw arcs centered at each end point of the segment so that the arcs cross above and below the segment; 2) connect the two points where the arcs cross.
2. Bisecting an Angle
1. Using a ruler, draw an angle similar to the
one below on the back of this paper .
2. Using only a compass and straight edge,
bisect the angle you have drawn.
HINT: To bisect an angle, the student should: 1) draw an arc centered at the angles vertex, so that the arc crosses both rays of the angle; 2) let the points where this arc crosses each ray be the centers for two new arcs, draw the new arcs without readjusting the compass, so that they cross inside the angle; 3) connect the vertex of the angle with the points where the two arcs cross. This line bisects the angle.
3. Angle Construction
1. Using only a compass and straight edge, construct a triangle with angles 30°, 60°, and
90°. On the back of this paper .
HINT: To draw a 30°, 60°, 90° triangle the students should 1) bisect a line segment as in Enrichment 1 (repeats Steps 1 and 2); 2) adjust the compass to draw an arc with a radius equal to the length of the line segment; 3) extend the segment bisector until it intersects the new arc; 4) connect the end of the segment with the bisector where it intersects the arc.
2. Using only a compass and straight edge, construct a triangle with angles 45°, 45°, and
90°. On the back of this paper.
HINT: To draw a 45°, 45°, 90° triangle the student should 1) bisect a line as in
Enrichment 1 (repeat Steps 1 and 2); 2) draw an arc with its center at the center of the bisected line and with a diameter equal to the entire line segment; 3) extend the segment bisector until it intersects the new arc; 4) connect the line segment and bisector as shown.