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…? HypothesisConclusion Corresponding Angles Postulate. Alternate Interior Angles Thm. Alternate Exterior Angles Thm. Same-Side Interior Angle Thm.

Find each angle measure. A. mECF B. mDCE mECF = 70° Corr.  s Post. 5x = 4x + 22 Corr.  s Post. x = 22 Subtract 4x from both sides. mDCE = 5x = 5(22) Substitute 22 for x. = 110°

Find m  QRS. m  QRS = 180° – x x = 118 m  QRS + 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. m  EDG B. m  BDG m  EDG = 75°Alt. Ext.  s Thm. m  BDG = 105° x – 30° = 75° Alt. Ext.  s Thm. x = 105Add 30 to both sides.

EXIT TICKET!

FYI ( SAFETY VALE )  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..