B Apply

9. Proof Given: ∠ S P T ≅ ∠ O P T , S P ¯ ≅ O P ¯ angle s p t approximately equal to . angle o p t comma . s p bar , approximately equal to . o p bar

   Prove: ∠ S ≅ ∠ O angle s approximately equal to . angle o

   

10. Proof Given: Y T ¯ ≅ Y P ¯ , ∠ C ≅ ∠ R , y t bar , approximately equal to . y p bar , comma . angle c approximately equal to , angle r comma

    ∠ T ≅ ∠ P angle t approximately equal to . angle p

    Prove: C T ¯ ≅ R P ¯ c t bar , approximately equal to . r p bar

    

Reasoning Copy and mark the figure to show the given information. Explain how you would prove ∠ P ≅ ∠ Q . angle p approximately equal to angle q .

11. Given: P K ¯ ≅ Q K ¯ , K L ¯ p k bar , approximately equal to . q k bar , comma . k l bar  bisects ∠ P K Q angle p k q
12. Given: K L ¯ k l bar  is the perpendicular bisector of P Q ¯ . p q bar , .
13. Given: K L ¯ ⊥ P Q ¯ , K L ¯ k l bar , up tack . p q bar , comma . k l bar  bisects ∠ P K Q angle p k q

    

14. Think About a Plan The construction of a line perpendicular to line l through point P on line l is shown. Explain why you can conclude that C P ↔ modified c p with left right arrow above  is perpendicular to l.
    • How can you use congruent triangles to justify the construction?
    • Which lengths or distances are equal by construction?
    • 
15. Proof Given: B A ¯ ≅ B C ¯ , B D ¯ b eh bar , approximately equal to . b c bar , comma . b d bar  bisects ∠ A B C angle eh b c

    Prove: B D ¯ ⊥ A C ¯ , B D ¯ b d bar , up tack . eh c bar , comma . b d bar  bisects A C ¯ eh c bar

    

16. Proof Given: l ⊥ A B ¯ , l up tack . eh b bar , comma  l bisects A B ¯ eh b bar  at C, P is on l

    Prove: P A = P B p eh equals p b

    

17. Constructions The construction of ∠ B angle b  congruent to given ∠ A angle eh  is shown. A D ¯ ≅ B F ¯ eh d bar , approximately equal to . b f bar  because they are congruent radii. D C ¯ ≅ F E ¯ d c bar , approximately equal to . f e bar  because both arcs have the same compass settings. Explain why you can conclude that ∠ A ≅ ∠ B . angle eh approximately equal to angle b .

    

18. Proof Given: B E ¯ ⊥ A C ¯ , D F ¯ ⊥ A C ¯ , B E ¯ ≅ D F ¯ , A F ¯ ≅ C E ¯ b e bar , up tack . eh c bar , comma . d f bar , up tack . eh c bar , comma . b e bar , approximately equal to . d f bar , comma . eh f bar , approximately equal to . c e bar

    Prove: A B ¯ ≅ C D ¯ eh b bar , approximately equal to . c d bar

    

19. Proof Given: J K ¯ | | Q P ¯ , J K ¯ ≅ P Q ¯ j k bar . vertical line vertical line , q p bar , comma . j k bar , approximately equal to . p q bar

    Prove: K Q ¯ k q bar  bisects J P ¯ . j p bar , .

    

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