See Problem 3.

13. Developing Proof Complete the two-column proof by filling in the blanks.

    

    Given: ∠ N ≅ ∠ S , angle n approximately equal to . angle s comma

    line l bisects T R ¯ t r bar  at Q

    Prove: Δ N Q T ≅ Δ S Q R cap delta n q t approximately equal to cap delta s q r

    Statements	Reasons
    1) ∠ N ≅ ∠ S angle n approximately equal to . angle s	1) Given
    2) ∠ N Q T ≅ ∠ S Q R angle n q t approximately equal to . angle s q r	2) a. __?__
    3) Line l bisects T R ¯ t r bar  at Q.	3) b. __?__
    4) c. __?__	4) Definition of bisect
    5) Δ N Q T ≅ Δ S Q R cap delta n q t approximately equal to cap delta s q r	5) d. __?__

14. Proof Given: ∠ V ≅ ∠ Y , angle v approximately equal to . angle y comma

    W Z ¯ w z bar  bisects ∠ V W Y angle v w y

    Prove: Δ V W Z ≅ Δ Y W Z cap delta v w z approximately equal to cap delta y w z

15. Proof Given: P Q ¯ ⊥ Q S ¯ , R S ¯ ⊥ S Q ¯ , p q bar , up tack . q s bar , comma . r s bar , up tack . s q bar , comma

    T is the midpoint of P R ¯ p r bar

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

See Problem 4.

Determine whether the triangles must be congruent. If so, name the postulate or theorem that justifies your answer. If not, explain.

B Apply

19. Proof Given: ∠ N ≅ ∠ P , M O ¯ ≅ Q O ¯ angle n approximately equal to . angle p comma . m o bar , approximately equal to . q o bar

    Prove: Δ M O N ≅ Δ Q O P cap delta m o n approximately equal to cap delta q o p

20. Proof Given: ∠ F J G ≅ ∠ H G J , F G ¯ ║ J H ¯ angle f j g approximately equal to . angle h g j comma . f g bar , box drawings double vertical , j h bar

    Prove: Δ F G J ≅ Δ H J G cap delta f g j approximately equal to cap delta h j g

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