Find lengths using Theorem 10.14

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Presentation transcript:

Find lengths using Theorem 10.14 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.

EXAMPLE 1 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

Standardized Test Practice 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.

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

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

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

Find lengths using Theorem 10.16 EXAMPLE 3 Find lengths using Theorem 10.16 Use the figure at the right to find RS. SOLUTION RQ2 = RS RT Use Theorem 10.16. 162 = x (x + 8) Substitute. 256 = x2 + 8x Simplify. = x2 + 8x – 256 Write in standard form. x –8 + 82 – 4(1) (– 256) 2(1) = Use quadratic formula. x = – 4 + 4 17 Simplify.

EXAMPLE 3 Find lengths using Theorem 10.16 Use the positive solution, because lengths cannot be negative. So, x 12.49, and RS 12.49 = – 4 + 4 17

GUIDED PRACTICE for Example 3 4. Find the value of x. x = 2 ANSWER

GUIDED PRACTICE for Example 3 5. Find the value of x. x = 24 5 ANSWER

GUIDED PRACTICE for Example 3 6. Find the value of x. x = 8 ANSWER

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

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

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

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

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.

Solve a real-world problem 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.

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

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

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

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

Daily Homework Quiz Find the value of x. Round to the nearest tenth,if necessary. 4. ANSWER 20.25

Daily Homework Quiz Find the value of x. Round to the nearest tenth,if necessary. 5. ANSWER 11.3