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For Exercises 12-15, use the given information. Which lines in the figure can you conclude are parallel?
For Exercises 12-15, use the given information. Which lines in the figure can you conclude are parallel? State the theorem that justifies each answer. SEE EXAMPLES 1 AND 3.
12. ∠2 ≅ ∠3
13. ∠6 ≅ ∠7
14. ∠1 ≅ ∠4
15. m∠5 + m∠8 = 180°
16. Write a flow proof of the Converse of the Alternate Exterior Angles Theorem. SEE EXAMPLE 2.
Use the diagram for Exercises 17 and 18. SEE EXAMPLE 2.
17. Given a ∥ b and b ∥ c, write a flow proof of Theorem 2-8.
18. Given a ∥ d and b ∥ d, write a flow proof of Theorem 2-9.
19. For what value of x is f ∥ g? Which theorem justifies your answer? SEE EXAMPLE 5.
20. Copy the diagram from Exercise 19. Construct a line parallel to line g. SEE EXAMPLE 4.
12. ∠2 ≅ ∠3
13. ∠6 ≅ ∠7
14. ∠1 ≅ ∠4
15. m∠5 + m∠8 = 180°
16. Write a flow proof of the Converse of the Alternate Exterior Angles Theorem. SEE EXAMPLE 2.
Use the diagram for Exercises 17 and 18. SEE EXAMPLE 2.
17. Given a ∥ b and b ∥ c, write a flow proof of Theorem 2-8.
18. Given a ∥ d and b ∥ d, write a flow proof of Theorem 2-9.
19. For what value of x is f ∥ g? Which theorem justifies your answer? SEE EXAMPLE 5.
20. Copy the diagram from Exercise 19. Construct a line parallel to line g. SEE EXAMPLE 4.