Geometry Honors – Study Guide Name ________________________ Pd ____Chapter 3 – Parallel and Perpendicular Lines

3-1 Lines and Angles and 3-2 Properties of Parallel LinesDefinition Symbol Use the picture below:

Parallel Lines

Skew Lines

Parallel Planes

Coplanar

Parallel lines are coplanar.Which planes containAB?

Note: Sometimes you will need to visualize a plane that is not shown in the picture. Explain...

Definition Name the lineTransversal

Definition Name the ∠ s Interior AnglesExterior AnglesAlternate Interior AnglesSame-Side Interior Angles

(Also called Consecutive Angles)

Corresponding AnglesAlternate Exterior Angles

Spec

ial A

ngle

Pai

rs w

/ Par

alle

l Lin

es

Definition Name the ∠ s

Interior Angles

Exterior Angles

Alternate Interior AnglesSame-Side Interior Angles

Corresponding Angles

Alternate Exterior Angles

Postulate 3-1 – Same-Side Interior Angles Postulate

If a transversal intersects two parallel lines, then same-side interior angles are supplementary.

Name the angles:

Theorem 3-1 Alternate Interior Angles Theorem

If a transversal intersects two parallel lines, then alternate interior angles are congruent.

Name the angles:

Theorem 3-2 Corresponding Angles Theorem

If a transversal intersects two parallel lines, then corresponding angles are congruent.

Name the angles:

Theorem 3-3Alternate Exterior Angles Theorem

If a transversal intersects two parallel lines, then alternate exterior angles are congruent.

Name the angles:

Using the picture to the above right... If m∠6 is 65º, then give the measures of the other angles and justify how you know this is true.m∠2 is _______ because_________________________________________________________m∠5 is _______ because _________________________________________________________m∠8 is _______ because _________________________________________________________m∠4 is _______ because__________________________________________________________3-3 Proving Lines ParallelTheorem 3-4 – Converse of the Corresponding Angles Theorem

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.

Theorem 3-5 Converse of the Alternate Interior Angles Theorem

If two lines and a transversal form alternate interior angles that are congruent, then the two lines are parallel.

Theorem 3-6Converse of the Same-Side Interior Angles Postulate

If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel.

Theorem 3-7Converse of the Alternate Exterior Angles Theorem

If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel.

Proofs - Two-Column

Proof- Paragraph

Proof- Flow Proof

(see below)

Flow Proof This includes arrows that show the logical connections between the statements with the reasons written below the statements.

3-7 Equations of Lines in the Coordinate PlaneSlope

4 Main Slopes of Lines

Slope Intercept Form and Point-Slope Form

Forms of Linear Equations

Reminders: How do you use the Slope-Intercept Form to graph a line?

How do you create a Point-Slope Form from 2 points?

How do you change a Point-Slope Form to a Slope-Intercept Form?

How do you find the slope or y-intercept from a standard equation of Ax + By = C?

3-4 Parallel and Perpendicular Lines and3-8 Slopes of Parallel and Perpendicular LinesTheorem 3-8 If two lines are parallel to the same line, then they are

parallel to each other.

Explain your thoughts:

Theorem 3-9 In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

Explain your thoughts:

Theorem 3-10

In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.

Explain your thoughts:

Slopes of Parallel Lines If two nonvertical lines are parallel, then their slopes are ____________. If the slopes of two distinct nonvertical lines are equal, then the lines are ________. Any two vertical lines or horizontal lines are _____________.

Slopes of Perpendicular Lines If two nonvertical lines are perpendicular, then the product of their slopes is ___________. If the slopes of two lines have a product of -1, then the lines are ______________________. Any horizontal lines and vertical line are ________________________.

3-5 Parallel Lines and TrianglesPostulate 3-2 Parallel Postulate

Through a point NOT on a line, there is one and only one line parallel to the given line.

Theorem 3-11Triangle Angle-Sum Theorem

The sum of the measures of the angles of a triangle is 180º.

Do the activity at the top of page 171.

Auxiliary Line A line that you can add to a diagram to help explain relationships in proofs.

Explain how PR can help to prove thatm∠ A+m∠B+m∠C=180 °?

Exterior Angle of a Polygon

An angle formed by a side and an extension of an adjacent side.

Remote Interior Angles

The two nonadjacent interior angles to an exterior angle of a triangle

Theorem 3-12Triangle Exterior Angle Theorem

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

m∠1=m∠2+m∠3