**Butterflies, Pinwheels, & Wallpaper**

**Symmetry and Transformations**

Problem 3.5

Focus Question:

When two parallel lines are cut by a transversal, what can be said about the angles formed? What is always true about the angle measures in a triangle? How do you know that your answers are correct?

8.G.A (.1, .1a, .1b)

Understand congruence and similarity using physical models, transparencies, or geometry software.

Do Now

Parallel Lines & Transversal

Parallel lines, transversals,

and angle sums

(Take notes during

this discussion.)

8.G.A (.1, .1a, .1b)

Understand congruence and similarity using physical models, transparencies, or geometry software

8.G.A (.1, .1a, .1b)

Understand congruence and similarity using physical models, transparencies, or geometry software

8.G.A (.1, .1a, .1b)

Understand congruence and similarity using physical models, transparencies, or geometry software

8.G.A (.1, .1a, .1b)

Understand congruence and similarity using physical models, transparencies, or geometry software

8.G.A (.1, .1a, .1b)

Understand congruence and similarity using physical models, transparencies, or geometry software

I

Complete the following:

Point C is a reflection of _______.

Point A is a reflection of _______.

Point M is the reflection of _______.

AC is a reflection of ____, which means that their lengths are ______.

CM is a reflection of _____, so each has a length of _____.

AM is the reflection of ______.

CB is perpendicular to _____, so AMC and AMB are ___________.

BAM CAM, so each angle measures ______.

C B, and each angle measures _________________________________.

Any Questions?????

(Take notes during

this discussion.)

Supplementary Angles - two angles whose measure adds up to a straight line or 180 degrees.

Complementary Angles - two angles whose measure adds up to 90 degrees.

Vertical Angles - angles that are opposite of each other when two lines cross.

Alternate Interior Angles - angles on opposite sides of the transversal, but inside the parallel lines.

Alternate Exterior Angles - angles on opposite sides of the transversal, but outside the parallel lines.

Parallel Lines - two lines

that do not intersect or

touch at any point.

Transversal - a line that

crosses, at least two,

other lines

Parallel lines cut by a transversal creates many angles with

special relationships.

Independent Practice

Using what you have learned about the angle

relationships created by parallel lines and a

transversal, identify the measure of each angle

and explain how you are able to identify the

measurement.