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Parallel Lines and Transversals

- Geometry
- Chapter 3.3
- NCSCOS 2.02

Essential Question

- What are the conclusions you get from

intersections of two parallel lines by a

transversal?

Parallel Lines and Transversals

Objective Students will be able to solve for

missing angles using the properties of

transversals

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Angles and Parallel Lines Activity

- Using a ruler, trace over two of the parallel

lines on your index card that are near the middle

of the card and about an inch apart. - Draw a transversal that makes clearly acute and

clearly obtuse angles near the center of the card - Label the angles with numbers from 1 to 8
- Sketch the parallel lines, transversal, and

number labels in your notes. We will use this to

record observations.

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Angles and Parallel Lines Activity

- Cut the index card carefully along the lines you

first drew to make six pieces. - Try stacking different numbered angles onto each

other and see what you observe. - Try placing different numbered angles next to

each other and see what you Observe - Mark your observations on the sketch in your

notes

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Angles and Parallel Lines Activity

- Answer the following questions
- How many different sizes of angles where formed?
- 2
- What special relationships exist between the

angles - Congruent and supplementary
- Indicate the two different sizes of angles in

your sketch.

Angles and Parallel Lines Activity

- How can we use the vocabulary learned Friday, to

describe these relationships? - IF parallel lines are cut by a transversal, THEN

- corresponding angles are congruent (Postulate in

Text) - alternate interior angles are congruent (Theorem

in Text) - alternate exterior angles are congruent (Theorem

in Text) - Consecutive Interior angles are Supplementary

(Theorem in Text)

Perpendicular Transversal

- In your notes, trace over two of the parallel

lines about one inch apart. - Using a protractor, draw a line perpendicular to

one of the parallel lines. - Extend this perpendicular so that it crosses the

other parallel line. - Based on your observations in the previous

exercise, what should be true about the new

angles formed? - Verify this with your protractor.
- If a line is perpendicular to one of two parallel

lines, then it is perpendicular to the other.

(Theorem in Text)

Postulate 15 Corresponding Angles

- If two parallel lines are cut by a transversal,

then the pairs of corresponding angles are

congruent.

Alternate interior Angles Theorem 3.4

- If two parallel lines are cut by a transversal,

then the pairs of alternate interior angles are

congruent.

Same-Side Interior Angles Theorem 3.5

- If two parallel lines are cut by a transversal,

then the pairs of consecutive interior angles are

supplementary. Measure of lt7 plus measure of lt8

equals 180 degrees.

Alternate Exterior Angles Theorem 3.6

- If two parallel lines are cut by a transversal,

then the pairs of alternate exterior angles are

congruent.

Perpendicular Transversal Theorem 3.7

- If a transversal is perpendicular to one of two

parallel lines, then it is perpendicular to the

other.

Frayer Model

Alternate Exterior Angles

Alternate Interior Angles

Corresponding Angles

Consecutive Interior Angles