1. Find lengths using Theorem 10.14
EXAMPLE 1
Find lengths using Theorem 10.14
ALGEBRA
Find ML and JK.
SOLUTION
NK NJ
= NL NM
Use Theorem
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.

2. EXAMPLE 1
Find lengths using Theorem 10.14
Find ML and JK by substitution.
SOLUTION ML
= ( x + 2 ) + ( x + 1) JK
= x + ( x + 4) = =
= 7
= 8

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

4. GUIDED PRACTICE for Examples 1 and 2 Find the value(s) of x. SOLUTION
= (6 + 9)
Use Theorem 90
= 5x + 25
Simplify.
13 = x
Solve for x

5. GUIDED PRACTICE for Examples 1 and 2 Find the value(s) of x. SOLUTION
= (4) (6)
Substitute.
3x = 24
Simplify.
x = 8
Solve for x.

6. GUIDED PRACTICE for Examples 1 and 2 Find the value(s) of x. SOLUTION
= (x+1)(x x – 1)
Use Theorem
3x + 15
= 2x2 + 2x
Simplify.
0 = 2x2 – x – 15
Combine Like Terms.
0 = (x – 3) (2x + 5)
Solve for x
3 = x
Use positive solution