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Understanding Angles Formed by Parallel Lines and a Transversal

This lesson aims to explore and apply theorems related to the angles formed by parallel lines and a transversal. We start with a warm-up to create and measure angles, facilitating the discovery of angle relationships. As we delve into the concepts, we will derive theorems based on given angle measurements and solve for unknown values using corresponding, alternate interior, and exterior angles. This learning culminates in an exit ticket reflecting on the historical significance of these theorems, attributed to Euclid, emphasizing their relevance in modern applications like engineering and design.

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Understanding Angles Formed by Parallel Lines and a Transversal

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Presentation Transcript

  1. 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?

  2. Warm up

  3. Creating Parallel line!

  4. Now • First number each angle • Next use your protractor to measure each angle you have created. • Have you discovered anything?

  5. Make your own theorem

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

  7. Find mQRS. x = 118 Corr. s Post. mQRS + x = 180° Def. of Linear Pair Subtract x from both sides. mQRS = 180° – x = 180° – 118° Substitute 118° for x. = 62°

  8. Find each angle measure. A. mEDG mEDG = 75° Alt. Ext. s Thm. B. mBDG x – 30° = 75° Alt. Ext. s Thm. x = 105 Add 30 to both sides. mBDG = 105°

  9. Exit ticket!

  10. 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..

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