WarmUp 1 Exercises EXAMPLE Find lengths using Theorem

Warm-Up 1 Exercises EXAMPLE Find lengths using Theorem 10. 14 Find ML and JK. SOLUTION NK NJ = NL NM x (x + 4) = (x + 1) (x + 2) x 2 + 4 x = x 2 + 3 x + 2 4 x = 3 x + 2 x = 2 Use Theorem 10. 14. Substitute. Simplify. Subtract x 2 from each side. Solve for x.

Warm-Up 1 Exercises EXAMPLE Find lengths using Theorem 10. 14 Find ML and JK by substitution. SOLUTION ML = ( x + 2 ) + ( x + 1) JK = x + ( x + 4) = 2+2+2+1 = 2+2+4 = 7 = 8

Warm-Up 2 Exercises EXAMPLE Standardized Test Practice SOLUTION RQ RP = RS 4 (5 + 4) = 3 RT (x + 3) 36 = 3 x + 9 9 = x ANSWER Use Theorem 10. 15. Substitute. Simplify. Solve for x The correct answer is D.

Warm-Up Exercises GUIDED PRACTICE Find the value(s) of x. ANSWER 13 = x for Examples 1 and 2

Warm-Up Exercises GUIDED PRACTICE Find the value(s) of x. ANSWER x = 8 for Examples 1 and 2

Warm-Up Exercises GUIDED PRACTICE Find the value(s) of x. ANSWER 3 = x for Examples 1 and 2

Warm-Up 3 Exercises EXAMPLE Find lengths using Theorem 10. 16 Use the figure at the right to find RS. SOLUTION RQ 2 = RS RT 162 = x Use Theorem 10. 16. (x + 8) Substitute. = x 2 + 8 x Simplify. 0 = x 2 + 8 x – 256 Write in standard form. x = – 8 + 256 x 82 – 4(1) (– 256) = – 4 + 4 17 2(1) Use quadratic formula. Simplify.

Warm-Up 3 Exercises EXAMPLE Find lengths using Theorem 10. 16 Use the positive solution, because lengths cannot be negative. So, x = – 4 + 4 17 12. 49, and RS 12. 49

Warm-Up Exercises GUIDED PRACTICE 4. Find the value of x. ANSWER x =2 for Example 3

Warm-Up Exercises GUIDED PRACTICE 5. Find the value of x. ANSWER x = 24 5 for Example 3

Warm-Up Exercises GUIDED PRACTICE 6. Find the value of x. ANSWER x =8 for Example 3

Warm-Up Exercises GUIDED PRACTICE for Example 3 7. Determine which theorem you would use to find x. Then find the value of x. ANSWER x = – 7 + 274

Warm-Up Exercises GUIDED PRACTICE for Example 3 8. Determine which theorem you would use to find x. Then find the value of x. ANSWER x = 8

Warm-Up Exercises GUIDED PRACTICE for Example 3 8. Determine which theorem you would use to find x. Then find the value of x. ANSWER x = 16

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 ? ANSWER EC < EA

Warm-Up 4 Exercises EXAMPLE 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.

Warm-Up 4 Exercises EXAMPLE Solve a real-world problem SOLUTION DC DB = AD 2 83, 000 DB DB Use Theorem 10. 16. 203, 0002 Substitute. 496, 494 Solve for DB. ANSWER Cassini is about 500, 000 kilometers from Tethys.

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

Daily Homework Quiz Warm-Up Exercises Find the value of x. Round to the nearest tenth, if necessary. 1. ANSWER 2

Daily Homework Quiz Warm-Up Exercises Find the value of x. Round to the nearest tenth, if necessary. 2. ANSWER 9

Daily Homework Quiz Warm-Up Exercises Find the value of x. Round to the nearest tenth, if necessary. 3. ANSWER 15

Daily Homework Quiz Warm-Up Exercises Find the value of x. Round to the nearest tenth, if necessary. 4. ANSWER 20. 25

Daily Homework Quiz Warm-Up Exercises Find the value of x. Round to the nearest tenth, if necessary. 5. ANSWER 11. 3