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L1.20 - Transformations, Transversals, and Proof

Author:Ms. Leon-Guerrero (Ms. LG)

Learning Intentions and Success Criteria

We are learning to:
  • Prove (in writing) that when a transversal crosses parallel lines, alternate interior angles are congruent.
  • Prove that when a transversal crosses parallel lines, corresponding angles are congruent.
We are successful when we can:
  • Prove alternate interior angles are congruent.
  • Prove corresponding angles are congruent.

20.1: Math Talk: Angle Relationships

20.1: Math Talk: Angle Relationships

20.2: Make a Mark? Give a Reason.

1. Translate lines AE and CD by the directed line segment from B to C. Label the images of A, B, C, D, E as A’, B’, C’, D’, E’. 2. What is true about lines AE and A’E’? Explain your reasoning.

3. Take turns with your partner to identify congruent angles.

  • For each pair of congruent angles that you find, explain to your partner how you know the angles are congruent.
  • For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.

20.3: An Alternate Explanation

1. Rotate line AE by 180 degrees around point C. Label the images of A, B, C, D, E as A’, B’, C’, D’, E’. 2. What is true about lines AB and A’B’? Explain your reasoning.

3. Take turns with your partner to identify congruent angles.

  • For each pair of congruent angles that you find, explain to your partner how you know the angles are congruent.
  • For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.

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Learning Intentions and Success Criteria

We are learning to:
  • Prove (in writing) that when a transversal crosses parallel lines, alternate interior angles are congruent.
  • Prove that when a transversal crosses parallel lines, corresponding angles are congruent.
We are successful when we can:
  • Prove alternate interior angles are congruent.
  • Prove corresponding angles are congruent.
Image

Cool-Down: Transformations on Parallel Lines

1.

2.

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