Warm-Up

GeometryInscribed Angles and Other Relationships

VocabularyCentral Angle – an angle whose

vertex is on the center of a circle. The arc measure is equal to the measure of the central angle.

Inscribed Angle – an angle whose vertex is on a circle.

Intercepted Arc – the arc that lies between an inscribed angle.

Investigation Activity

Use trace paper to create angles RTS, RUS, and RVS.

Compare the four angles to each other (RPS, RTS, RUS, RVS). What do you notice?

Theorems

Draw a right triangle in your circle. How do you know it is a right triangle?

Draw a quadrilateral in your circle. What can you conclude about the angles of your quadrilateral?

Theorems

Practice

m∠BAC = m∠BAC = m∠BAC =

m∠BAC = = = 2=

Practice

y + 87° = 180° -87° -87°

y = 93°

2x + 100° = 180° -100° -100°

2x = 80°

x = 40

2y + 5x = 180°

2(60°-x) +5x = 180°

120° -2x +5x = 180°

3x = 60°

x = 20°

3y + 3x = 180°

y + x = 60°

y = 60° - x

y =60° - 20°

y =40°

10.4 – Other Relationships in Circles.

Practice

Since the intersection occurs inside of the circle. We add the two intercepted arcs formed by the angle and its vertical angle.

Practice

Since the intersection occurs outside of the circle. We subtract the arcs formed by the angle and then divide by two.

Practice

Since the intersection occurs outside of the circle. We subtract the arcs formed by the angle and then divide by two.

Practice

Practice

Exit TicketHomeworkCopy down

one of the pictures and examples that we completed in class and turn it in.

Pg. 617: 9-23 odd

Pg. 624: 9-27 odd