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Five-Minute Check (over Lesson 10–5)

NGSSS

Then/Now

New Vocabulary

Theorem 10.12

Example 1:Use Intersecting Chords or Secants

Theorem 10.13

Example 2:Use Intersecting Secants and Tangents

Theorem 10.14

Example 3:Use Tangents and Secants that Intersect Outside a Circle

Example 4:Real-World Example: Apply Properties of Intersecting Secants

Concept Summary: Circle and Angle Relationships

Over Lesson 10–5

A. yes

B. no

Determine whether BC is tangent to the given circle.___

A. A

B. B

A B

0%0%

Over Lesson 10–5

A. yes

B. no

Determine whether QR is tangent to the given circle.___

A. A

B. B

A B

0%0%

Over Lesson 10–5

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 10

B. 11

C. 12

D. 13

Find x. Assume that segments that appear to be tangent are tangent.

Over Lesson 10–5

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

Find x. Assume that segments that appear to be tangent are tangent.

A.

B.

C. 20

D.

Over Lesson 10–5

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

SL and SK are tangent to the circle. Find x.______

A. 1

B.

C. 5

D. 44

__5

2

MA.912.G.6.2 Define and identify: circumference, radius, diameter, arc, arc length, chord, secant, tangent and concentric circles.

MA.912.G.6.4 Determine and use measures of arcs and related angles.

Also addresses MA.912.G.6.3.

You found measures of segments formed by tangents to a circle. (Lesson 10–5)

• Find measures of angles formed by lines intersecting on or inside a circle.

• Find measures of angles formed by lines intersecting outside the circle.

• secant

Use Intersecting Chords or Secants

A. Find x.

Theorem 10.12

Substitution

Simplify.

Answer: x = 82

Use Intersecting Chords or Secants

B. Find x.

Theorem 10.12

Substitution

Simplify.

Step 1 Find mVZW.

Use Intersecting Chords or Secants

Step 2 Find mWZX.

WZX = 180 – VZW Definition of supplementaryangles

x = 180 – 79 Substitution

x = 101 Simplify.

Answer: x = 101

C. Find x.

Theorem 10.12

Substitution

Multiply each side by 2.

Use Intersecting Chords or Secants

Subtract 25 from each side.

Answer: x = 95

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 92

B. 95

C. 98

D. 104

A. Find x.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 92

B. 95

C. 97

D. 102

B. Find x.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 96

B. 99

C. 101

D. 104

C. Find x.

Use Intersecting Secants and Tangents

A. Find mQPS.

Theorem 10.13

Substitute and simplify.

Answer: mQPS = 125

B.

Theorem 10.13

Use Intersecting Secants and Tangents

Substitution

Multiply each side by 2.

Answer:

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 98

B. 108

C. 112.5

D. 118.5

A. Find mFGI.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 99

B. 148.5

C. 162

D. 198

B.

Use Tangents and Secants that Intersect Outside a Circle

A.

Theorem 10.14

Substitution

Multiply each side by 2.

Use Tangents and Secants that Intersect Outside a Circle

Subtract 141 from each side.

Multiply each side by –1.

Use Tangents and Secants that Intersect Outside a Circle

B.

Theorem 10.14

Substitution

Multiply each side by 2.

Use Tangents and Secants that Intersect Outside a Circle

Add 140 to each side.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 23

B. 26

C. 29

D. 32

A.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 194

B. 202

C. 210

D. 230

B.

Apply Properties of Intersecting Secants

Theorem 10.14

Substitution

Apply Properties of Intersecting Secants

Multiply each side by 2.

Subtract 96 from each side.

Multiply each side by –1.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 25

B. 35

C. 40

D. 45