22. Developing Proof Here is another way to prove the Isosceles Triangle Theorem. Supply the missing information.

    Begin with isosceles Δ H K J cap delta h k j  with K H ¯ ≅ K J ¯ . k h bar , approximately equal to . k j bar , .

    Draw a. __?__, a bisector of the base H J ¯ . h j bar , .

    Given: K H ¯ ≅ K J ¯ , k h bar , approximately equal to . k j bar , comma  b. __?__ bisects H J ¯ h j bar

    Prove: ∠ H ≅ ∠ J angle h approximately equal to . angle j

    

    Statements	Reasons
    1) K M ¯ k m bar  bisects H J ¯ . h j bar , .	1) c. __?__
    2) H M ¯ ≅ J M ¯ h m bar , approximately equal to . j m bar	2) d. __?__
    3) K H ¯ ≅ K J ¯ k h bar , approximately equal to . k j bar	3) Given
    4) K M ¯ ≅ K M ¯ k m bar , approximately equal to . k m bar	4) e. __?__
    5) Δ K H M ≅ Δ K J M cap delta k h m approximately equal to cap delta k j m	5) f. __?__
    6) ∠ H ≅ ∠ J angle h approximately equal to . angle j	6) g. __?__

23. Proof Supply the missing information in this statement of the Converse of the Isosceles Triangle Theorem. Then write a proof.

    Begin with Δ P R Q cap delta p r q  with ∠ P ≅ ∠ Q . angle p approximately equal to . angle q .

    Draw a. __?__, the bisector of ∠ P R Q . angle p r q .

    Given: ∠ P ≅ ∠ Q , angle p approximately equal to . angle q comma  b. __?__ bisects ∠ P R Q angle p r q

    Prove: P R ¯ ≅ Q R ¯ p r bar , approximately equal to . q r bar

    

24. Writing Explain how the corollaries to the Isosceles Triangle Theorem and its converse follow from the theorems.
25. Proof Given: A E ¯ ≅ D E ¯ , A B ¯ ≅ D C ¯ eh e bar , approximately equal to . d e bar , comma . eh b bar , approximately equal to . d c bar  Prove: Δ A B E ≅ Δ D C E cap delta eh b e approximately equal to cap delta d c e

    

26. Proof Prove Theorem 4-5. Use the diagram next to it on page 252.

27. 1. Communications In the diagram below, what type of triangle is formed by the cables of the same height and the ground?

       
       Image Long Description

    2. What are the two different base lengths of the triangles?
    3. How is the tower related to each of the triangles?
28. Algebra The length of the base of an isosceles triangle is x. The length of a leg is 2 x − 5 . 2 x minus 5 .  The perimeter of the triangle is 20. Find x.
29. Constructions Construct equiangular triangle ABC. Justify your method.

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