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Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Dec 31, 2015

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Page 1: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:
Page 2: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Five-Minute Check (over Lesson 10–2)

NGSSS

Then/Now

Theorem 10.2

Proof: Theorem 10.2 (part 1)

Example 1: Real-World Example: Use Congruent Chords to Find Arc Measure

Example 2: Use Congruent Arcs to Find Chord Lengths

Theorems

Example 3: Use a Radius Perpendicular to a Chord

Example 4: Real-World Example: Use a Diameter Perpendicular to a Chord

Theorem 10.5

Example 5: Chords Equidistant from Center

http://glencoe.mcgraw-hill.com/sites/0078884845/
Page 3: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Over Lesson 10–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 105

B. 114

C. 118

D. 124

http://glencoe.mcgraw-hill.com/sites/0078884845/
Page 4: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Over Lesson 10–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 35

B. 55

C. 66

D. 72

http://glencoe.mcgraw-hill.com/sites/0078884845/
Page 5: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Over Lesson 10–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 125

B. 130

C. 135

D. 140

http://glencoe.mcgraw-hill.com/sites/0078884845/
Page 6: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Over Lesson 10–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 160

B. 150

C. 140

D. 130

http://glencoe.mcgraw-hill.com/sites/0078884845/
Page 7: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Over Lesson 10–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 180

B. 190

C. 200

D. 210

http://glencoe.mcgraw-hill.com/sites/0078884845/
Page 8: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Over Lesson 10–2

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 129.6 ft

B. 165 ft

C. 259.2 ft

D. 345.6 ft

Dianne runs around a circular track that has a radius of 55 feet. After running three quarters of the distance around the track, how far has she run?

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Page 9: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

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.

Page 10: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

You used the relationships between arcs and angles to find measures. (Lesson 10–2)

• Recognize and use relationships between arcs and chords.

• Recognize and use relationships between arcs, chords, and diameters.

Page 11: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:
Page 12: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:
Page 13: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Use Congruent Chords to Find Arc Measure

Jewelry A circular piece of jade is hung from a

chain by two wires around the stone.

JM KL and = 90. Find .

Page 14: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Use Congruent Chords to Find Arc Measure

Page 15: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 42.5

B. 85

C. 127.5

D. 170

Page 16: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Use Congruent Arcs to Find Chord Lengths

Page 17: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Use Congruent Arcs to Find Chord Lengths

WX = YZ Definition of congruent segments

7x – 2 = 5x + 6 Substitution

2x = 8 Add 2 to each side.

x = 4 Divide each side by 2.

So, WX = 7x – 2 = 7(4) – 2 or 26.

Answer: WX = 26

Page 18: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 6

B. 8

C. 9

D. 13

Page 19: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:
Page 20: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Use a Radius Perpendicular to a Chord

Answer:

Page 21: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 14

B. 80

C. 160

D. 180

Page 22: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Use a Diameter Perpendicular to a Chord

CERAMIC TILE In the ceramic stepping stone

below, diameter AB is 18 inches long and chord EF

is 8 inches long. Find CD.

Page 23: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Use a Diameter Perpendicular to a Chord

Step 1 Draw radius CE.

This forms right ΔCDE.

Page 24: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Use a Diameter Perpendicular to a Chord

Step 2 Find CE and DE.

Since AB = 18 inches, CB = 9 inches. All

radii of a circle are congruent, so

CE = 9 inches.

Since diameter AB is perpendicular to EF,

AB bisects chord EF by Theorem 10.3. So,

DE = (8) or 4 inches.__12

Page 25: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Use a Diameter Perpendicular to a Chord

Step 3 Use the Pythagorean Theorem to find CD.

CD2 + DE2 = CE2

Pythagorean Theorem

CD2 + 42 = 92 Substitution

CD2 + 16 = 81 Simplify.

CD2 = 65 Subtract 16

from each side.Take the positive

square root.

Answer:

Page 26: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 3.87

B. 4.25

C. 4.90

D. 5.32

In the circle below, diameter QS is 14 inches long and chord RT is 10 inches long. Find VU.

Page 27: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:
Page 28: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Chords Equidistant from Center

Since chords EF and GH are congruent, they are

equidistant from P. So, PQ = PR.

Page 29: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

Chords Equidistant from Center

PQ = PR

4x – 3 = 2x + 3 Substitution

x = 3 Simplify.

So, PQ = 4(3) – 3 or 9

Answer: PQ = 9

Page 30: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. 7

B. 10

C. 13

D. 15

Page 31: Splash Screen. Lesson Menu Five-Minute Check (over Lesson 10–2) NGSSS Then/Now Theorem 10.2 Proof: Theorem 10.2 (part 1) Example 1: Real-World Example:

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