Inscribed Angles

Question 1

What is an inscribed angle?

What is the difference between a central angle and an inscribed angle?

Answer 1

An angle whose vertex is on a circle and whose sides contain chords of the circle

Central angle is from the origin of a circle

Question 2

What is Theorem 9-7?

Answer 2

The measure of an inscribed angle is equal to half the measure of its intercepted arc

Question 3

What is the first corollary of Theorem 9-7?

Answer 3

Corollary 1: if two inscribed angles intercept the sam arc, then the angles are congruent

Question 4

What is the second corollary of Theorem 9-7?

Answer 4

Corollary 2: An angle inscribed in a semicircle is a right angle

Question 5

What is the third corollary of Theorem 9-7?

Answer 5

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary

Question 6

What is Theorem 9-7 and the 3 corollaries?

Thm9-7: the measure of an inscribed angle is equal to half the measure of its intercepted arc

Corollary 1: if two inscribed angles intercept the same arc, then the angles ar congruent

Corollary 2: an angle inscribed in a semicircle is a right angle

Corollary 3: if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary

Question 7

What is Theorem 9-8?

Answer 7

The measure of an angle formed by a chord and a tangent is equal to half the measure of its intercepted arc