Class Opener: 𝐹𝑖𝑛𝑑 𝑚 𝐴𝐺 1.) 2.) 𝑊ℎ𝑎𝑡 𝑐𝑎𝑛 𝑦𝑜𝑢 𝑐𝑜𝑛𝑐𝑙𝑢𝑑𝑒 𝑎𝑏𝑜𝑢𝑡 𝑍𝑌 𝑎𝑛𝑑 𝑋𝑌 ? 3.) 𝐿𝑎𝑏𝑒𝑙 𝑒𝑎𝑐ℎ 𝑠𝑒𝑔𝑚𝑒𝑛𝑡 𝑏𝑒𝑙𝑜𝑤:

Agenda 1.) Warm Up 10.4 Tues 3/7 2.) Home Work Check Angle in Circles 3.) Agenda / Objectives 4.) Lesson with Guided Graphic Organizer 5.) Solutions to Problems 6.) Practice Work 7.) Scavenger Hunt – Inscribed Angles 10.4 Tues 3/7 Angle in Circles 10.5 Wed. 3/8 Segments in Circles 10.6 Thur. 3/9 Equations of Circles

Inscribed Angles

and whose sides are chords of the circle. Inscribed Angle: An angle whose vertex is on the circle INTERCEPTED ARC AND and whose sides are chords of the circle. INSCRIBED ANGLE

Determine if each angle is an inscribed angle Determine if each angle is an inscribed angle. Name the intercepted arc for the angle. 1. YES; CL C L O T

Determine whether each angle is an inscribed angle Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. NO; QVR 2. Q V K R S

What do we call this type of angle? The measure of the inscribed angle is HALF the measure of the intercepted arc! 𝑚Y= 1 2 𝑚 𝐴𝐵 120 A x B 𝑌= 60 0 y

So to find the measure of an intercepted arc… IF… THEN…

OPEN YOUR GRAPIC ORGANIZER Find the First Section 1.) Copy the first Theorem on pg. 613 2.) Read the theorem for understanding. 3.) Work the example.

40  112  M Q K S J 2 Examples: 3. If m 𝑱𝑲 = 80, find 𝒎JMK 4. If 𝑴𝑲𝑺 = 56, find 𝒎 𝑴𝑺 112 

If two inscribed angles intercept the same arc, then they are congruent. 𝟕𝟐 𝟎

3x = 9 x = 3 5x = 2x + 9 In J, 𝐦𝑸𝑻𝑫=5x and  𝑫𝑼𝑸 = 2x + 9. Example 5 Find the value of x. 5x = 2x + 9 3x = 9 x = 3

IN YOUR GRAPIC ORGANIZER Find the Second Section 1.) Copy Theorem 10.9 on pg. 614 2.) Read the theorem for understanding. 3.) Work the example.

If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle. 180 diameter

Example 6 In K, GH is a diameter and mGNH = 4x – 14. Find the value of x. 4x – 14 = 90 H K x = 26 N G

Example 7 In K, m1 = 6x – 5 and m2 = 3x – 4. Find the value of x. 6x – 5 + 3x – 4 = 90 H 2 K x = 11 1 N G

IN YOUR GRAPIC ORGANIZER Find the Third Section 1.) Copy Theorem 10.10 on pg. 615 2.) Read the theorem for understanding. 3.) Work the example.

If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

A circle can be circumscribed around a quadrilateral if and only if its opposite angles are supplementary. B A D C

y = 70 z = 95 110 + y =180 z + 85 = 180 Example 8 Find y and z. z 110

IN YOUR GRAPIC ORGANIZER Find the Fourth Section 1.) Copy Theorem 10.11 on pg. 615 2.) Read the theorem for understanding. 3.) Work the example.

Who was able to solve each problem? Volunteers…

Let's practice! 10.3 1 – 12 10.3,4 1 - 19

Scavenger Hunt: Circles 10.1 – 10.3