Inscribed Angle Theorem (Corollary 3) Cyclic Quadrilaterals
- Author:
- Tim Brzezinski
- Topic:
- Angles, Circle, Quadrilaterals
The following applet shows a quadrilateral that has been inscribed in a circle.
Recall what you've learned form the INSCRIBED ANGLE THEOREM (http://tube.geogebra.org/b/1457199#material/1473237).
This will help you discover yet a new corollary to this theorem.
Notice how the measures of angles A and C are shown. (A and C are opposite angles of a cyclic quadrilateral.) Complete the following:
1) How does the measure of angle A compare with the measure of arc BCD? Why is this?
2) How does the measure of angle C compare with the measure of arc BAD? Why is this?
3) What is the sum of the measures of arcs BCD & BAD? (This one's easy!)
4) According to your answers for (1), (2), & (3), what should the sum of the measures of angles A & C be?
5) Confirm your answer to (4) by clicking the checkbox in the lower right hand corner. (Be sure to move points B and D around after doing so!)
6) Click on the "Show measures of angles B & D" checkbox now.
7) How does the measure of angle B compare with the measure of arc ADC? Why is this?
8) How does the measure of angle D compare with the measure of arc ABC? Why is this?
9) What is the sum of the measures of arcs ADC & ABC? (This one's easy!)
10) According to your answers for (7), (8), & (9), what should the sum of the measures of angles B & D be?
11) Confirm your answer to (10) by clicking the checkbox in the lower right hand corner. (Be sure to move points A and C around after doing so!)
Complete the following corollary: If a quadrilateral is inscribed in a circle, then both pairs of opposite angles are...
Questions are located above the applet.