1. The points E, U, C, L, I and D are as shown:
Draw the following figures: a) EU- b) CL- and c) ID-.
2. Using the pints of question 1, draw the following: a) EL-, b) LC-, c) LD- and d) DL-.
3. Two intersecting circles determine a line, as shown as on the next column in the accompanying diagram. Draw three circles, where each circle intersects the other two circles, as in the example shown on the right. Next draw the three lines determined by each pair of intersecting circles. What conclusion is suggested by your drawing?
4. Use a compass to draw three circles of the same size through point A. Let B, K and L be the other of intersection of pair of circles. Now draw a fourth circle of the same size as the other three that passes through B and creates points of intersection M and N, as shown:
a) Draw the line KL- and MN-. What can you say about these two lines?
b) Draw the lines LM- and KN-. What can you say about these two lines?
c) Draw the line AB-. What connection does it seem to have to any of the lines drawn earlier?
5. Draw a circle with center at point A and a second circle of the same radius with centre at point B, where the radius is large enough to cause the circles to intersect at two points C and D. Let M be the point of intersection of CD- and AB-.
a) Use a protractor to measure the angle at m. What can you say about how CD- and AB- intersect?
b) Use a ruler to measure MA- and MB-. What can you say about point M?
6. Draw two circles, and locate four points on each circle. Draw the segment as shown:
a) Carefully measures the angles with vertices at A, B, C, and D with a protractor. What relationship do you see on the basis of your measurements?
b) Measure the angle with vertices at P, Q, R and S, and discuss what relationships hold among the angles in that figure.
7. The lines l and m are parallel. Find the measures of the numbered angle shown.
8. Find the measures of the numbered angles in the triangles shown.
9. Let PQ-||AB- and RQ-||AC-. Find the measurement of ∠1, ∠2, . . . , ∠8. Explain how you found your answers.
10. The incident (incoming) and reflected (outgoing) rays of a light beam make congruent angles with a flat mirror:
Suppose tow mirrors are perpendicular to one another. Show that, after the second reflected, the outgoing ray is parallel to the incoming ray.
11. Parallel lines p and q are cut by transversal t. In addition, m∠4 = m∠5 and m∠6 = m∠7.
What is the measure of ∠8.