Lesson 2:

Angles and Parallel Lines

Angles and Parallel Lines

Section 3.2

Virginia SOL Standard G.2.c

The student will use the relationships between angles formed by two lines cut by a transversal to solve real-world problems involving angles formed when parallel lines are cut by a transversal.

New Definitions

None Today

New Postulates

Postulate 3.1: Corresponding Angle Postulate

New Theorems

Theorem 3.1: Alternate Interior Angle Theorem

Theorem 3.2: Consecutive Interior Angles Theorem

Theorem 3.3: Alternate Exterior Angles Theorem

Theorem 3.4: Perpendicular Transversal Theorem

Lesson 2 Objectives

The student will be able to…

1.Use theorems to determine the relationships between specific pairs of angles.

2.Use Algebra to find angle measurement.

Postulate 3.1:

Corresponding Angle Postulate

Corresponding Angle Postulate

If two parallel lines are intersected by a transversal, then each pair of corresponding angles are congruent.

Transversals and Angle Pairs

Theorems are not to be feared.

Theorems may sound scary with all the syllables and words and punctuation, but…

Theorems are not the enemy.

Theorems only exist to make your life easier.

Theorem 3.1:

Alternate Interior Angle Theorem

Alternate Interior Angle Theorem

If two parallel lines are intersected by a transversal, then each pair of alternate interior angles is congruent.

Theorem 3.2:

Consecutive Interior Angles Theorem

Consecutive Interior Angles Theorem

If two parallel lines are intersected by a transversal, then each pair of consecutive interior angles is supplementary.

Theorem 3.3:

Alternate Exterior Angles Theorem

Alternate Exterior Angles Theorem

If two parallel lines are intersected by a transversal, then each pair of alternate exterior angles is congruent.

Theorem 3.4:

Perpendicular Transversal Theorem

Perpendicular Transversal Theorem

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

Now Apply the Thmeorems and Postulates

Transversals with parallel lines are very nice because any two angles are either congruent or supplementary.

Answer the A & B given the diagram:

Answer the A & B given the diagram:

Answer the A & B given the diagram:

Answer the A & B given the diagram:

Connecting Congruence with Measure

What does that look like with angle measures?

Fill in each angle with its measure

Fill in each angle with its measure

Fill in each angle with its measure

Let’s kick it up a notch!

Mr. Volk: How could we make this more fun?

Student: Oh, what if we put some variables in our diagrams?!

Mr. Volk: That is a great idea. Since you guys want to , let’s do some algebra.

Answer the A & B given the diagram:

Answer the A & B given the diagram:

Answer the A & B given the diagram:

Answer the A & B given the diagram:

Answer the A & B given the diagram:

Answer the A & B given the diagram:

Answer the A & B given the diagram:

Congruent or Supplementary?

Congruent or Supplementary?

Congruent or Supplementary?

Congruent or Supplementary?

Congruent or Supplementary?

Congruent or Supplementary?

Congruent or Supplementary?

Formative Assessment (pop quiz)

Take out a clean sheet of paper

•Your name

•Today’s date

•Block Number

•TITLE: Transversals Pop Quiz

•You may use your Postulates and Theorems Packet

•You may not use your Notes Packet

Transversals Pop Quiz

Transversals Pop Quiz

Transversals Pop Quiz

Transversals Pop Quiz

Transversals Pop Quiz Answers

Homework

p. 181-182 – #1-29 odd,

p. 184 – #47

DUE TUESDAY 10/1

View the full PowerPoint for this lesson here:

https://drive.google.com/file/d/0B-ni1paLPjNsZ3dWVUMyTnEyNTg/edit?usp=sharing