Practice and Problem-Solving Exercises

A Practice

See Problem 1.

6. A carpenter is building a trellis for vines to grow on. The completed trellis will have two sets of diagonal pieces of wood that overlap each other.

   

   1. If pieces A, B, and C must be parallel, what must be true of ∠ 1 , ∠ 2 , angle 1 comma angle 2 comma  and ∠ 3 ? angle 3 question mark
   2. The carpenter attaches piece D so that it is perpendicular to piece A. If your answer to part (a) is true, is piece D perpendicular to pieces B and C? Justify your answer.

See Problem 2.

7. Developing Proof Copy and complete this paragraph proof of Theorem 3-7 for three coplanar lines.

   Given: l || k l vertical linevertical line k  and m || k m vertical linevertical line k

   Prove: l || m l vertical linevertical line m

   Proof: Since l || k , ∠ 2 ≅ ∠ 1 l vertical linevertical line k comma angle 2 approximately equal to angle 1  by the a. ? ¯ modified question mark with under bar below Postulate. Since m || k , m vertical linevertical line k comma  b. ? ¯ modified question mark with under bar below ≅ approximately equal to  c. ? ¯ modified question mark with under bar below for the same reason. By the Transitive Property of Congruence, ∠ 2 ≅ ∠ 3 . angle 2 approximately equal to angle 3 .  By the d. ? ¯ modified question mark with under bar below Postulate, l || m . l vertical linevertical line m .

   

8. Proof Write a paragraph proof.

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

   Prove: a || d eh vertical linevertical line d

   

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