Apply the Corresponding Angles Converse

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Presentation transcript:

Apply the Corresponding Angles Converse EXAMPLE 1 Apply the Corresponding Angles Converse ALGEBRA Find the value of x that makes m n. SOLUTION Lines m and n are parallel if the marked corresponding angles are congruent. (3x + 5)o = 65o Use Postulate 16 to write an equation 3x = 60 Subtract 5 from each side. x = 20 Divide each side by 3. The lines m and n are parallel when x = 20.

GUIDED PRACTICE for Example 1 Is there enough information in the diagram to conclude that m n? Explain. ANSWER Yes. m n because the angle corresponding to the angle measuring 75o also measures 75o since it forms a linear pair with the 105o angle. So, corresponding angles are congruent and Postulate 16 says the lines are parallel.

GUIDED PRACTICE for Example 1 Explain why Postulate 16 is the converse of Postulate 15. ANSWER Postulate 16 switches the hypothesis and conclusion of Postulate 15.