OBJECTIVE: PROVE AND USE THEOREMS ABOUT THE ANGLES FORMED BY PARALLEL LINES AND A TRANSVERSAL. WARM UP: ON HANDOUT

Who, When, Where, and Why Parallel?

WARM UP

CREATING PARALLEL LINE!

NOW

First number each angle

Next use your protractor to measure each angle you have created.

Have you discovered anything?

MAKE YOUR OWN THEOREM

Theorem

If…?, then…?

Hypothesis

Conclusion

Corresponding Angles Postulate.

Alternate Interior Angles Thm.  

Alternate Exterior Angles Thm.  

Same-Side Interior Angle Thm.  

Find each angle measure.A. mECF

B. mDCE

mECF = 70° Corr. s Post.

5x = 4x + 22 Corr. s Post.x = 22 Subtract 4x from both sides.

mDCE = 5x= 5(22) Substitute 22 for x.= 110°

Find mQRS.

mQRS = 180° – x

x = 118mQRS + x = 180°

Corr. s Post.

= 180° – 118° = 62°

Subtract x from both sides.Substitute 118° for x.

Def. of Linear Pair

Find each angle measure.

A. mEDG

B. mBDG

mEDG = 75°Alt. Ext. s Thm.

mBDG = 105°

x – 30° = 75°

Alt. Ext. s Thm.x = 105Add 30 to both sides.

EXIT TICKET!

FYI ( S A F E T Y V A L E)The theorems we used today, were first established 2,300 years ago by this genius guy named Euclid.

Something that has stand the test of time has to be important, right?

Where are parallel lines used that make them important?

You like cars? Etc..