B Apply

9. Think About a Plan One traditional type of log cabin is a single rectangular room. Suppose you begin building a log cabin by placing four logs in the shape of a rectangle. What should you measure to guarantee that the logs on opposite walls are parallel? Explain.
   • What type of information do you need to prove lines parallel?
   • How can you use a diagram to help you?
   • What do you know about the angles of the geometric shape?

10. Proof Prove the Perpendicular Transversal Theorem (Theorem 3-9): In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other.

    

    Given: In a plane, a ⊥ b eh up tack b  and b || c . b vertical linevertical line c .

    Prove: a ⊥ c eh up tack c

The following statements describe a ladder. Based only on the statement, make a conclusion about the rungs, one side, or both sides of the ladder. Explain.

11. The rungs are each perpendicular to one side.
12. The rungs are parallel and the top rung is perpendicular to one side.
13. The sides are parallel. The rungs are perpendicular to one side.
14. Each side is perpendicular to the top rung.
15. The rungs are perpendicular to one side. The sides are not parallel.

16. Public Transportation The map below is a section of a subway map. The yellow line is perpendicular to the brown line, the brown line is perpendicular to the blue line, and the blue line is perpendicular to the pink line. What conclusion can you make about the yellow line and the pink line? Explain.

    

17. Writing Theorem 3-8 states that in a plane, two lines perpendicular to the same line are parallel. Explain why the phrase in a plane is needed. (Hint: Refer to a rectangular solid to help you visualize the situation.)
18. Quilting You plan to sew two triangles of fabric together to make a square for a quilting project. The triangles are both right triangles and have the same side and angle measures. What must also be true about the triangles in order to guarantee that the opposite sides of the fabric square are parallel? Explain.

C Challenge

For Exercises 19–24, a, b, c, and d are distinct lines in the same plane. For each combination of relationships, tell how a and d relate. Justify your answer.

19. a || b , b || c , c || d eh vertical linevertical line b comma b vertical linevertical line c comma c vertical linevertical line d
20. a || b , b || c , c ⊥ d eh vertical linevertical line b comma b vertical linevertical line c comma c up tack d
21. a || b , b ⊥ c , c || d eh vertical linevertical line b comma b up tack c comma c vertical linevertical line d
22. a ⊥ b , b || c , c || d eh up tack b comma b vertical linevertical line c comma c vertical linevertical line d
23. a || b , b ⊥ c , c ⊥ d eh vertical linevertical line b comma b up tack c comma c up tack d
24. a ⊥ b , b || c , c ⊥ d eh up tack b comma b vertical linevertical line c comma c up tack d

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