Section Name: Proofs with Transversals 2 Warm Up Section Name: Proofs with Transversals 2

Converses Converse: Switching the hypothesis and conclusion of a conditional statement. For our proofs last class what was always our given? What were we trying to prove? Now we want to prove the opposite so what will we need to be given? What will we be trying to prove?

Converses Converse: Switching the hypothesis and conclusion of a conditional statement.  Corresponding Angles Postulate: If two lines are parallel, then their corresponding angles are congruent. Converse of the Corresponding Angles Postulate : Consecutive Interior Angles Theorem: Given two lines are parallel, then their consecutive interior angles are supplementary. Converse of the Consecutive Interior Angles Theorem:

Application Which of the following statements will justify that 𝑚∥𝑛, explain. a. ∠5 and ∠6 are supplementary. b. ∠3 and ∠6 are congruent. c. m∠4+𝑚∠6=180 d. ∠2 and ∠3 are congruent. e. ∠1 and ∠6 are congruent.

Matching Activity You will each be given a set of four diagrams.  Each of the different diagrams are labelled A, B, C, or D. I will put a statement on the board.  You will decide which diagram matches the statement.  You will then write the letter for that diagram on your whiteboard and hold it up for me to check. Once everyone has answered we will discuss the answer(s) as a class.

Every diagram tells its own story… 𝑳𝑴 ∥ 𝑵𝑶 by the converse of the alternate interior angles theorem.

Every diagram tells its own story… ∠𝑳𝑹𝑺 is supplementary to ∠𝑹𝑺𝑵 by the consecutive interior angles theorem.

Every diagram tells its own story… ∠𝑷𝑹𝑴≅∠𝑹𝑺𝑶 by the corresponding angles theorem.

Every diagram tells its own story… 𝑳𝑴 ∥ 𝑵𝑶 by the alternate interior angles theorem.

Every diagram tells its own story… 𝑳𝑴 ∥ 𝑵𝑶 by the converse of the alternate exterior angles theorem.

Every diagram tells its own story… ∠𝑷𝑹𝑳≅∠𝑸𝑺𝑶 by the alternate exterior angles theorem.

Every diagram tells its own story… 𝑳𝑴 ∥ 𝑵𝑶 by the converse of the corresponding angles theorem.

Every diagram tells its own story… 𝑳𝑴 ∥ 𝑵𝑶 by the converse of the consecutive interior angles theorem.

Section Name: Unit 3 Review Warm-up Solve for all missing angle measures. Given: 𝑈𝑇 ∥ 𝑉𝑃 𝑚∠2=55° 𝑚∠8=82° Section Name: Unit 3 Review

Complete the following proofs: Warm-Up Complete the following proofs: Given: ∠4≅∠5. Prove: 𝑚∥𝑛 Given:𝑚∥𝑛 Prove:∠4≅∠5. Review Day Notes

Warm-Up Solve for all missing angle measures. 𝑚∠2=61° 𝑚∠13= 107°

What is enough information to prove that lines are perpendicular? What is enough information to prove that lines are parallel?

Practicing the transitive property. ∠𝐴≅∠𝐵 ∠𝐵≅∠𝐶 ∠ ≅∠ ∠1≅∠3 ∠ ≅∠ ∠1≅∠5 ∠ ≅∠ ∠6≅∠7 ∠2≅∠7

Warm-Up Test Today Name all the different angle relationships. Give an example. State whether they are congruent or supplementary. T S R 2 1 4 3 5 6 7 8 Test Today

Given 𝑦∥𝑧 and the measure of ∠2=58° ∠13=111° ∠10=69° Find the measure of ALL other angles.