Inscribed Angle Theorems

Name the inscribed angle in this diagram

•  $\angle ABC$  

•  $\angle CPA$  

•  $\angle APC$  

Tags

CCSS.HSG.C.A.2

What is an inscribed angle?

• an angle whose vertex is on the circle

• an angle whose vertex is on the center of the circle

• an angle whose vertex is outside the circle

What is the name of this theorem?

The measure of an inscribed angle equals half the measure of the intercepted arc.

• The Inscribed Angle Theorem

• The Central Angle Theorem

• The Arc Theorem

Which phrases completes this theorem correctly?

The measure of an inscribed angle equals ....

• half the measure of the intercepted arc.

• twice the measure of the intercepted arc.

• the measure of the intercepted arc.

Which two sets of angles in this diagram are congruent?

•  $\angle ABD\ \cong\ \angle DCA$  

•  $\angle BDC\ \cong\ \angle BAC$  

•  $\angle ACD\ \cong\ \angle BAC$  

•  $\angle CPD\ \cong\ \angle BPC$  

Tags

CCSS.HSG.CO.C.9

Which phrase completes this theorem correctly?

If two inscribed angles intersect the same arc, then ...

• they are congruent

• they are similar

• they are right angles

Which corollary is illustrated by this example?

• An angle inscribed in a semicircle is a right angle.

• If a quadrilateral is inscribed in a circle then it is a parallelogram.

• Arcs are congruent if and only if their corresponding inscribed angles are congruent.

What is the measure of  $\angle BAC$  ?

•  $m\angle BAC\ =90$  

•  $m\angle BAC\ =180$  

•  $m\angle BAC\ =360$  

Tags

CCSS.HSG.C.A.2

CCSS.HSG.C.A.3

Which corollary is illustrated by this example?

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

• Arcs are congruent if and only if their corresponding central angles are congruent.

• An angle inscribed in a semicircle is a right angle.

Tags

CCSS.HSG.C.A.2

Which phrase completes this theorem correctly?

If a parallelogram is inscribed in a circle, then ...

• it is a rectangle

• is is a trapezoid

• it always has four congruent sides