Ch 4 - Parallels

4.1 – Parallel Lines and Planes

Parallel Lines:

Parallel Planes:

Skew Lines:

Example: Name the parts of the prism shown below. Assume segments that look parallel are parallel.

All planes parallel to plane SKL.

All segments that intersect

All segments parallel to

All segments skew to

Example: Name all parts of the figure.

All planes parallel to plane ABF.

All segments that intersect

All segments parallel to

All segments skew to

4.2 – Parallel Lines and Transversals

Transversal:

Angles Formed by a Transversal:

Interior Angles –

Exterior Angles –

Alternate Interior Angles –

Alternate Exterior Angles –

Consecutive Interior Angles –

Example: Identify each pair of angles as alternate interior, alternate exterior, consecutive interior, or vertical.

Hands-On Geometry: P149Follow directions on notebook paperAnswer questions here:

Special Angle Theorems:

Theorem 4.1: Alternate Interior Angles Theorem

Theorem 4.2: Consecutive Interior Angles Theorem

Theorem 4.3: Alternate Exterior Angles Theorem

Example: If , find .

Example: If , find , , and .

Example: In the figure below, a||b and k is a transversal. Find and .

4.3 – Transversals and Corresponding Angles

Corresponding Angles:

Postulate 4.1 – Corresponding Angles:

Example: Lines a and b are cut by transversal c. Name two pairs of corresponding angles.

Example:In the figure, a||b, and k is a transversal. Which angle is congruent to ? Explain your answer.

Find the measure of if .

Concept Summary

Types of angle pairs formed when a transversal cuts two parallel lines.Congruent Supplementary

Theorem 4.4 – Perpendicular Transversal:

Example: If , find x.

4.4 – Proving Lines Parallel

Postulate 4-2:

Theorem 4-5:

Theorem 4-6:

Theorem 4-7:

Theorem 4-8:

Summary of 5 ways to prove lines parallel:

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-

-

-

-

Example:

If and , find x so that a||b.

Example:

Find the value of x so that .

Example:

Identify the parallel segments in the letter E.

4.5 – Slope

Slope –-

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-

Slope:

Example: Find the slope of each line.

Types of slope:

Postulate 4-3:

Postulate 4-4:

Example:

4.6 – Equations of Lines

Linear Equation:

Slope-Intercept Form:

Example: Name the slope and y-intercept of the graph of each equation.

y = 2/3 x + 6

y = 0

x = 7

3y + 12 = 6x

Example: Graph 2x – y = 4 using the slope and the y-int.

Example: Graph –x + 3y = 9 using the slope and y-int.

Example: Write an equation of the line parallel to the graph of y = -2x + 3 that passes through the point at (0, 1).

Example: Write an equation of the line perpendicular to the graph of y = 3x + 4 that passes through the point at (6, 9).