Cogito
Geometry · Chapter 6 · Lesson 2
Inscribed Angles
Half the central angle, wherever you stand.
11 problems · about 23 minutes · G-C.A.2
What this lesson teaches
The student applies the inscribed angle theorem and its corollaries.
- An inscribed angle is half the central angle on the same arc.
- Its size does not depend on where the vertex sits.
- An angle inscribed in a semicircle is always a right angle.
Warm Up
Straightforward practice. Get the method working first.
4 problemsCentral 90°. Inscribed on the same arc?
Answer 45
Why 45°.
Central 140°. Inscribed on the same arc?
Answer 70
Why Half.
Inscribed 35°. Central on the same arc?
Answer 70
Why Double.
Cyclic quadrilateral, one angle 85°. Its opposite, in degrees?
Answer 95
Why They add to 180.
Build It Up
The same ideas with more to keep track of.
3 problemsTwo inscribed angles on the same arc, one is 25°. The other?
Answer 25
Why Equal.
Angle in a semicircle, in degrees?
Answer 90
Why Always a right angle.
Select every true statement about inscribed angles.
Answer They are half the central angle on the same arc.; An angle in a semicircle is a right angle.
Why Position on the arc is irrelevant.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsCentral 200°. Inscribed on the same arc?
Answer 100
Why Half.
Cyclic quadrilateral, one angle 110°. Its opposite?
Answer 70
Why 180 − 110.
Halving: Central angle 80°. Inscribed angle on the same arc, in degrees?
Answer 40
Why 40°.
The Semicircle: An angle inscribed in a semicircle, in degrees?
Answer 90
Why 90°.