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Warm-Up Exercises EXAMPLE 1 Find lengths using Theorem 10.14 Find ML and JK. SOLUTION NK NJ = NL NM Use Theorem 10.14. x (x + 4) = (x + 1) (x + 2) Substitute. x 2 + 4x = x 2 + 3x + 2 Simplify. 4x = 3x + 2 Subtract x 2 from each side. x = 2 Solve for x.

EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

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Page 1: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises EXAMPLE 1 Find lengths using Theorem 10.14

Find ML and JK.

SOLUTION

NK NJ = NL NM Use Theorem 10.14.

x (x + 4) = (x + 1) (x + 2) Substitute.

x2 + 4x = x2 + 3x + 2 Simplify.

4x = 3x + 2 Subtract x2 from each side.

x = 2 Solve for x.

Page 2: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises EXAMPLE 1 Find lengths using Theorem 10.14

Find ML and JK by substitution.

ML = ( x + 2 ) + ( x + 1)

= 2 + 2 + 2 + 1

= 7

JK = x + ( x + 4)

= 2 + 2 + 4

= 8

SOLUTION

Page 3: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises EXAMPLE 2 Standardized Test Practice

SOLUTION

RQ RP = RS RT Use Theorem 10.15.

4 (5 + 4) = 3 (x + 3) Substitute.

36 = 3x + 9 Simplify.

9 = x Solve for x

ANSWER The correct answer is D.

Page 4: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2

Find the value(s) of x.

13 = x

ANSWER

Page 5: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2

Find the value(s) of x.

x = 8 ANSWER

Page 6: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Examples 1 and 2

Find the value(s) of x.

3 = x ANSWER

Page 7: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises EXAMPLE 3 Find lengths using Theorem 10.16

Use the figure at the right to find RS.

SOLUTION

256 = x2 + 8x

0 = x2 + 8x – 256

RQ2 = RS RT

162 = x (x + 8)

x –8 + 82 – 4(1) (– 256) 2(1)

=

x = – 4 + 4 17

Use Theorem 10.16.

Substitute.

Simplify.

Write in standard form.

Use quadratic formula.

Simplify.

Page 8: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises EXAMPLE 3 Find lengths using Theorem 10.16

Use the positive solution, because lengths cannot be negative.

= – 4 + 4 17 So, x 12.49, and RS 12.49

Page 9: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Example 3

Find the value of x. 4.

x = 2 ANSWER

Page 10: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Example 3

Find the value of x. 5.

x = 24 5

ANSWER

Page 11: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Example 3

Find the value of x. 6.

x = 8 ANSWER

Page 12: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Example 3

Determine which theorem you would use to find x. Then find the value of x.

7.

x = – 7 + 274 ANSWER

Page 13: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Example 3

Determine which theorem you would use to find x. Then find the value of x.

8.

x = 8 ANSWER

Page 14: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Example 3

Determine which theorem you would use to find x. Then find the value of x.

8.

x = 16 ANSWER

Page 15: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Example 3

9. In the diagram for Theorem 10.16, what must be true about EC compared to EA ?

EC < EA

ANSWER

Page 16: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises EXAMPLE 4 Solve a real-world problem

SCIENCE

Tethys, Calypso, and Telesto are three of Saturn’s moons. Each has a nearly circular orbit 295,000 kilometers in radius. The Cassini-Huygens spacecraft entered Saturn’s orbit in July 2004. Telesto is on a point of tangency. Find the distance DB from Cassini to Tethys.

Page 17: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises EXAMPLE 4 Solve a real-world problem

SOLUTION

DC DB = AD2 Use Theorem 10.16.

83,000 DB 203,0002 Substitute.

DB 496,494 Solve for DB.

ANSWER

Cassini is about 500,000 kilometers from Tethys.

Page 18: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises GUIDED PRACTICE for Examples 4

11. Why is it appropriate to use the approximation symbol in the last two steps of the solution to Example 4?

Since the distances given are not exact, it is appropriate to use the approximation symbol in the solution.

ANSWER

Page 19: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises Daily Homework Quiz

ANSWER 2

1.

Find the value of x. Round to the nearest tenth,if necessary.

Page 20: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises Daily Homework Quiz

2.

Find the value of x. Round to the nearest tenth,if necessary.

ANSWER 9

Page 21: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises Daily Homework Quiz

3.

Find the value of x. Round to the nearest tenth,if necessary.

ANSWER 15

Page 22: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises Daily Homework Quiz

4.

Find the value of x. Round to the nearest tenth,if necessary.

ANSWER 20.25

Page 23: EXAMPLE 1 Warm-Up Exercises Find lengths using Theorem 10Aug 10, 2015  · EXAMPLE 2 Warm-Up Exercises Standardized Test Practice SOLUTION RQ RP = RS RT Use Theorem 10.15. 4 (5 + 4)

Warm-Up Exercises Daily Homework Quiz

5.

Find the value of x. Round to the nearest tenth,if necessary.

ANSWER 11.3


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