Relationships of Angles Day 1
Objectives: Have the students discover four theorems about
angles in circles.
Theorem 1: If an angle is inscribed in a circle, then it's measure is half the measure of its intercepted arc. m<ACE = 1/2m<ABC 

Theorem 2: If two inscribed angles of a circle intercept the same arc, then the angles are congruent. m<ABC = m<ADC 

Theorem 3: If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle. conversely, if one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is the right angle. m<ABC = 90^{o} if and only if AC is the diameter of the circle 

Theorem 4: A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. m<ABC + m<CDA = 180^{o} m<BCD + m<DAB = 180^{o} 
For the GSP activity click here. Here are the interactive GSP sketches for each of the theorems: Theorem 1, Theorem 2, Theorem 3, Theorem 4.
Conclusion: Have the students discuss the conclusions they
were able to form based on the activity. Discuss the theorems
that the students should have found during the activity.
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Next: Day 6
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Katherine Huffman