TODAY IN GEOMETRY…

Warm up: Inscribed Polygons

STATs for Ch.10 Quiz

Learning Target : 10.5 You will find the measures of angles inside or outside of a circle

Independent practice

WARM UP: Find the value(s) of the variable(s).

1. 2. 3.

HOW DID YOU “SHAPE” UP??Results for ALL of my Geometry classes:

GRADE NUMBER OF STUDENTS WHO TOOK THE CH.10 QUIZ (16 pts.)

1ST PERIOD 3RD PERIOD 5TH PERIOD 6TH PERIOD TOTAL

A 15 18 18 17 68B 3 5 3 6 19C 0 0 0 0 0D 2 3 0 0 5F 2 0 4 0 6

Avg. 14.11 14.52 14.26 15.09 14.50

THEOREM-CHORDS AND TANGENTS: If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of the intersected arc.

2 1

𝐴

𝐵𝐶

PRACTICE:

PRACTICE:

12

(210 ° )=𝟏𝟎𝟓° 2 (98 ° )=𝟏𝟗𝟔° 2 (80 ° )=𝟏𝟔𝟎°

INTERSECTING LINES AND CIRCLES: If two lines intersect a circle, there are three places where the lines can intersect:

𝑶𝑵 h𝑡 𝑒𝑐𝑖𝑟𝑐𝑙𝑒

𝑰𝑵𝑺𝑰𝑫𝑬 h𝑡 𝑒𝑐𝑖𝑟𝑐𝑙𝑒

𝑶𝑼𝑻𝑺𝑰𝑫𝑬 h𝑡 𝑒𝑐𝑖𝑟𝑐𝑙𝑒

INSIDE ANGLE THEOREM: If two chords intersect inside a circle, then the measure of each angle is one half the sum (addition) of the measures of the arcs intercepted by the angle and its vertical angle.

𝐶𝐵

𝐴

𝐷

12

EXAMPLE:

PRACTICE: Find the value of x.

Use Inside Angle Theorem:

EXAMPLE: Find the value of y.

Find the value of the missing angle: Use Inside Angle Theorem:

2 ∙ ∙2

PRACTICE: Find the value of x.

Find the value of the missing angle: Use Inside Angle Theorem:

2 ∙ ∙2

25 °137 °

𝑥 °43 °

OUTSIDE ANGLE THEOREM: If two lines intersect outside a circle, then the measures of the angle formed is one-half the difference (subtract) of the measures of the intercepted arc.

𝐶

𝐵

𝐴

1

𝑅

𝑄𝑃

2

𝑌

𝑋𝑊3𝑍

EXAMPLE:

EXAMPLE: Find the value of x.

Find the missing arc measure: Use Outside Angle Theorem:

110°

EXAMPLE: Find the value of a.

Use Outside Angle Theorem:

∙22 ∙

PRACTICE: Find the value of x.

Use Outside Angle Theorem:

∙22 ∙

EXAMPLE: Find the value of x.

Use Outside Angle Theorem:

∙22 ∙

EXAMPLE: Find the value of x.

Use Outside Angle Theorem:

∙22 ∙

61 °(5 𝑥−1)°(10 𝑥+1)°

PRACTICE: Find the value of x.

Use Outside Angle Theorem:

∙22 ∙

5 4 °(5 𝑥+14)°(13 𝑥−6)°

HOMEWORK #5:

Pg. 683: 3-13

If finished, work on other assignments:

HW #1: Pg. 655: 3-20, 24-26, 30HW #2: Pg. 661: 3-14, 17, 23HW #3: Pg. 667: 3-15HW #4: Pg. 676: 3-16 Pg. 679: 40-46