today in geometry… review: finding inside and outside angles of circles warm up: finding angles ...

TODAY IN GEOMETRY…

Review: Finding inside and outside angles of circles

Warm up: Finding angles

Learning Target : 10.6 You will find lengths of segments in a circle

Independent practice

REVIEW: So far we have learned to find ANGLES of the following circles and intersecting lines.

𝑥

𝑥

𝑥

𝑥

INSIDE ANGLE:

OUTSIDE ANGLE:

INSCRIBED ARC:

MINOR ARC:

REVIEW: Solve for x.

𝑥

36 °126 °

𝑥 142 °118°

2 𝑥+6

4 𝑥−6

∙22 ∙

We reviewed how to find ANGLES of intersecting lines and circles.

NOW…we will find LENGTHS of segments of intersecting lines and

circles!

SEGMENTS OF A CHORD THEOREM: The products of segments of two intersecting chords are equal.

𝑐

𝑎𝑑

𝑏𝑎 ∙𝑏¿𝑐 ∙𝑑

EXAMPLE: Find x.

Use Segments of a Chord Theorem Multiply

Divide

8 96

𝑥

PRACTICE: Find x.

Use Segments of a Chord Theorem Multiply

Divide

8 4

14𝑥

EXAMPLE: Find x.

Use Segments of a Chord Theorem Distribute

Subtract

Subtract

Divide

3 5

𝑥+1 𝑥+7

PRACTICE: Find x.

Use Segments of a Chord Theorem Distribute

Subtract

Subtract

Divide

78

2 𝑥+43 𝑥+1

SEGMENTS OF SECANTS THEOREM: The product of one of the whole segment and the exterior segment of the secant is equal to the product of the other whole segment and the exterior segment of the secant.

𝑑𝑐

𝑎

𝑏

𝐸

𝑎 ∙(𝑎+𝑏)¿𝑐 ∙(𝑐+𝑑)

EXAMPLE: Find x.

Use Segments of a Secant Theorem Distribute and Simplify

Multiply Subtract

Divide

PRACTICE:

Use Segments of Secants Theorem Distribute and Simplify

Multiply Subtract

Divide

EXAMPLE: Find x.

Use Segments of a Secant Theorem Combine like terms

Distribute Subtract

Subtract

Divide

EXAMPLE: Find x.

Use Segments of a Secant Theorem Combine like terms

Distribute Subtract

Subtract

Divide

SEGMENTS OF SECANTS AND TANGENTS: The square of the segment of the tangent is equal to the product of the whole segment and the exterior segment of the secant.

𝑐𝑏

𝑎

𝐸

𝑎2¿𝑏 ∙(𝑏+𝑐)

EXAMPLE: Find x.

Use Segments of a Secant & Tangents Square and Distribute

Subtract

Divide

𝑥8

16

EXAMPLE: Find x.

Use Segments of a Secant & Tangents Square and Distribute

Subtract

Divide

EXAMPLE: Find x.

Use Segments of a Secant & Tangents Add and Multiply

Square root

PRACTICE: Find x.

Use Segments of a Secant & Tangents Add and Multiply

Square root

𝑥

214

EXAMPLE: Find x.

Use Segments of a Secant & Tangents Distribute

FOIL Subtract

Subtract

Divide

PRACTICE: Find x.

Use Segments of a Secant & Tangents Distribute

FOIL Subtract

Subtract

HOMEWORK #6:

Pg. 692: 3, 4, 6, 9-14

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: 40-46HW #5: Pg. 683: 3-13