5 - Minute Check x + 20 = 52 - 20 -20 x = 32 If Josh needs an umbrella, then it is raining.

Think about the converses of the statements Objective(s): Students will analyze & apply angle relationships to prove lines are parallel. Why? So you can apply the converses of angle relationships to real world situations. Mastery is 80% or better on 5-minute checks. -Corresponding angles (corr. ’s ) -Alternate Interior angles (alt. int. ’s ) -Alternate Exterior angles (alt. ext. ’s ) -Consecutive Interior AKA Same Side Interior angles (SSI ’s are supp.) Think about the converses of the statements

Postulate 16: Corresponding Angles Converse If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

This is not an angle measure!!! Skill Development Solve for x. This is not an angle measure!!!

Skill Develop Prove the corresponding Angles Converse Given: 1  2 Prove: m ║ n m 3 2 1 n Statements: 1  2 2  3 1  3 m ║ n Reasons: Given Vertical Angles Transitive prop. Corresponding angles converse

Proof of the Alt. Interior Angles Converse Given: 4 and 5 are supplementary Prove: g║h 6 g h 5 4 You can write a paragraph proof, 1 sentence per step You are given that 4 and 5 are supplementary. By the Linear Pair Postulate, 5 and 6 are also supplementary because they form a linear pair. By the Congruent Supplements Theorem, it follows that 4  6. Therefore, by the Alternate Interior Angles Converse, g and h are parallel.

Think…..Ink….Share Find the value of x that makes j║k. Solution: Lines j and k will be parallel if the marked angles are supplementary. So by the SSI converse x + 4x = 180  5x = 180  x = 36  4x = 144  So, if x = 36, then j║k. x 4x

If you were thinking corr ’s converse, think again. YES!! Consec Int ’s converse YES!! Alt. Int. ’s converse NO!! If you were thinking corr ’s converse, think again. 82+40≠120

Choose the Word That Best completes the sentence.

Guided Practice X = 43 X = 90 X = 38

Performance Task Explain your reasoning.. X = 100 X = 70 X = 48

Exit Slip 1= 100 & 2 = 100 1 & 2 Correspond 1= 75 2= 75 1=2 & 2 = 75 1 = 2 vertical 1 = 135 correspond

What was today’s objective(s)??? Objective(s): Students will analyze & apply angle relationships to prove lines are parallel. Why? So you can apply the converses of angle relationships to real world situations. Mastery is 80% or better on 5-minute checks.

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