Practice and Problem-Solving Exercises

A Practice

See Problems 1 and 2.

Developing Proof Complete the following coordinate proofs.

4. The diagonals of an isosceles trapezoid are congruent.

   

   Given: Trapezoid EFGH with E F ¯ ≅ G H ¯ e f bar , approximately equal to , g h bar

   Prove: E G ¯ ≅ F H ¯ e g bar , approximately equal to , f h bar

   1. Find EG.
   2. Find FH.
   3. Explain why E G ¯ ≅ F H ¯ . e g bar , approximately equal to , f h bar , .

5. The medians drawn to the congruent sides of an isosceles triangle are congruent.

   

   Given: Δ PQR cap delta  with P Q ¯ ≅ R Q ¯ , p q bar , approximately equal to , r q bar , comma  M is the midpoint of P Q ¯ , p q bar , comma  N is the midpoint of R Q ¯ r q bar

   Prove: P N ¯ ≅ R M ¯ p n bar , approximately equal to , r m bar

   1. What are the coordinates of M and N?
   2. What are PN and RM?
   3. Explain why P N ¯ ≅ R M ¯ . p n bar , approximately equal to , r m bar , .

B Apply

Tell whether you can reach each type of conclusion below using coordinate methods. Give a reason for each answer.

6. A B ¯ ≅ C D ¯ eh b bar , approximately equal to , c d bar
7. A B ¯ ∥ C D ¯ eh b bar , parallel to , c d bar
8. A B ¯ ⊥ C D ¯ eh b bar , up tack , c d bar
9. A B ¯ eh b bar  bisects C D ¯ . c d bar , .
10. A B ¯ eh b bar  bisects ∠ CAD. angle , cap ccap acap d.
11. ∠ A ≅ ∠ B angle , eh approximately equal to , angle b
12. ∠ A angle eh  is a right angle.
13. A B + B C = A C eh b plus b c equals eh c
14. Δ ABC cap delta  is isosceles.
15. Quadrilateral ABCD is a rhombus.
16. A B ¯ eh b bar  and C D ¯ c d bar  bisect each other.
17. ∠ A angle eh  is the supplement of ∠ B . angle b .
18. A B ¯ , C D ¯ , eh b bar , comma . c d bar , comma  and E F ¯ e f bar  are concurrent.

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