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: P149
Follow directions on notebook paper
Answer 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:
-
-
-
-
-
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 –
-
-
-
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).