Angles Inscribed to a Semicircle



The objective of this activity is to find the measures of inscribed angles intersecting a semicircle.
Instructions 1. Given points A, B, C, and D on Circle O where segment AB is a diameter. 2. Form angle ACB where C is its vertex and CA and CB are its sides. 3. Form angle ADB where D is its vertex and DA and DB are its sides. 3. Find the measures of angles ACB and ADB. 4. Answer the follow-up questions.

Given segment AB is a diameter, what kind of arc is arc AB? (Please review basics of circles)

What do you observe with the measures of angles ACB and ADB?

Move vertices C and D along the circle, is there any changes on the measures angles ACB and ADB?

Based on your observations on angles ACB and ADB, what can you conclude to angles inscribed to a semicircle?