3-3 Slopes of Lines. CCSS Content Standards G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

3-3 Slopes of Lines

CCSS

Content StandardsG.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).Mathematical Practices4 Model with mathematics.7 Look for and make use of structure.8 Look for and express regularity in repeated reasoning.

Then/Now

You used the properties of parallel lines to determine congruent angles.

• Find slopes of lines.

• Use slope to identify parallel and perpendicular lines.

Vocabulary

• slope

• rate of change

Concept

Concept

A.

B.

C.

D.

Example 1aA. Find the slope of the line.

A. 0

B. undefined

C. 7

D.

Example 1bB. Find the slope of the line.

A.

B.

C. –2

D. 2

Example 1cC. Find the slope of the line.

A. 0

B. undefined

C. 3

D.

Example 1dD. Find the slope of the line.

Concept

Example 3Determine Line Relationships

Step 1 Find the slopes of and .

Determine whether and are parallel, perpendicular, or neither for F(1, –3), G(–2, –1), H(5, 0), and J(6, 3). Graph each line to verify your answer.

Example 3Determine Line Relationships

Step 2 Determine the relationship, if any, between thelines.

The slopes are not the same, so and are not parallel. The product of the slopes is

So, and are not

perpendicular.

Example 3Determine Line Relationships

Answer: The lines are neither parallel nor perpendicular.

Check When graphed, you can see that the lines arenot parallel and do not intersect in right angles.

Example 3

A. parallel

B. perpendicular

C. neither

Determine whether AB and CD are parallel, perpendicular, or neither for A(–2, –1), B(4, 5), C(6, 1), and D(9, –2)