Practice and Problem-Solving Exercises

A Practice

See Problem 1.

8. Developing Proof Complete the flow proof.

   Given: P S ¯ ≅ P T ¯ , ∠ P R S ≅ ∠ P R T p s bar , approximately equal to . p t bar , comma . angle p r s approximately equal to . angle p r t

   Prove: Δ P R S ≅ Δ P R T cap delta p r s approximately equal to cap delta p r t

   

   
   Image Long Description

9. Developing Proof Complete the paragraph proof.

   

   Given: ∠ A angle eh  and ∠ D angle cap d  are right angles, A B ¯ ≅ D E ¯ eh b bar , approximately equal to . d e bar

   Prove: Δ A B E ≅ Δ D E B cap delta eh b e approximately equal to cap delta d e b

   Proof: It is given that ∠ A angle eh  and ∠ D angle cap d  are right angles. So, a. __?__ by the definition of right triangles. b. __?__, because of the Reflexive Property of Congruence. It is also given that c. __?__. So, Δ A B E ≅ Δ D E B cap delta eh b e approximately equal to cap delta d e b  by d. __?__.

10. Proof Given: H V ¯ ⊥ G T ¯ , G H ¯ ≅ T V ¯ , h v bar , up tack . g t bar , comma . g h bar , approximately equal to . t v bar , comma  I is the midpoint of H V ¯ h v bar

    Prove: Δ I G H ≅ Δ I T V cap delta i g h approximately equal to cap delta i t v

    

See Problem 2.

11. Proof Given: P M ¯ ≅ R J ¯ , P T ¯ ⊥ T J ¯ , R M ¯ ⊥ T J ¯ , p m bar , approximately equal to . r j bar , comma . p t bar , up tack . t j bar , comma . r m bar , up tack . t j bar , comma  M is the midpoint of T J ¯ t j bar

    Prove: Δ P T M ≅ Δ R M J cap delta p t m approximately equal to cap delta r m j

    

B Apply

Algebra For what values of x and y are the triangles congruent by HL?

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14. Study Exercise 8. Can you prove that Δ P R S ≅ Δ P R T cap delta p r s approximately equal to cap delta p r t  without using the HL Theorem? Explain.

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