Chapter 10.5: Inscribed Angles

Question 1

Inscribed angles

Answer 1

an angle is an inscribed angle of a circle if its vertex is on the circle and its sides are chords of the circle.

Question 2

Intercepted arc

Answer 2

the arc that lies in the interior of an inscribed angle is its intercepted arc.

Question 3

Thm. 10.9

Answer 3

if an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc.

Question 4

Thm. 10.10

Answer 4

if two inscribed angles of a circle intercept the same arc, then the angles are congruent.

Question 5

Thm. 10.11

Answer 5

an angle that is inscribed in a circle is a right angle if and only if its corresponding arc is a semicircle.

Question 6

Thm. 10.12

Answer 6

a quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.