Inscribed Angles Geometry 11-3

Inscribed Angle Investigation Using geometry tools, or a calculator Draw a large circle Create a central angle and an inscribed angle that share the same points on the circle Compare the measures Inscribed Angle Investigation

Inscribed Angle Theorem The measure of an angle inscribed in a circle is half the measure of its intercepted arc Inscribed Angle Theorem

Inscribed Angle Theorem

Inscribed Angle Investigation Based on this last conjecture, what can do we know about an inscribed angle that intercepts a diameter of the circle? Inscribed Angle Investigation

Angle Inscribed in a Semicircle Corollary Angles inscribed in a semicircle are right angles Angle Inscribed in a Semicircle Corollary

Inscribed Angle Investigation Using geometry tools, or a calculator Create a second inscribed angle with a different vertex, but with the same intercepted arc as before What can you conclude about the measures of the two angles? Inscribed Angle Investigation

Inscribed Angles Intercepting Arc Corollary Inscribed angles that intercept the same arc are congruent Inscribed Angles Intercepting Arc Corollary

Cyclic Quadrilateral Investigation Cyclic Quadrilateral - A quadrilateral inscribed in a circle Construct a large cyclic quadrilateral Compare the measures of the angles Cyclic Quadrilateral Investigation

Cyclic Quadrilateral Conjecture The opposite angles in a cyclic quadrilateral are supplementary Cyclic Quadrilateral Conjecture

Inscribed Angles

Thought Investigation Imagine an inscribed angle, which we know is half the intercepted arc Thought Investigation

Thought Investigation One endpoint of the inscribed angle is on a tangent line Thought Investigation

Thought Investigation Move the vertex of the inscribed angle toward the tangent line, the angles value does not change, half the intercepted arc. Thought Investigation

Thought Investigation So what happens when the vertex reaches the tangent point? Thought Investigation

Inscribed angles

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Practice Problems

Pages 601 – 605 6 – 24 even, 33 – 35, 51 – 53 Homework