21. Think About a Plan While helping your family clean out the attic, you find the piece of paper shown below. The paper contains clues to locate a time capsule buried in your backyard. The maple tree is due east of the oak tree in your backyard. Will the clues always lead you to the correct spot? Explain.

    
    Image Long Description

    • How can you use a diagram to help you?
    • What type of geometric figure do the paths and the marked line form?
    • How does the position of the marked line relate to the positions of the angles?
22. Constructions Use a straightedge to draw a triangle. Label it Δ J K L . cap delta j k l .  Construct Δ M N P ≅ Δ J K L cap delta m n p approximately equal to cap delta j k l  so that the triangles are congruent by ASA.

23. Reasoning Can you prove that the triangles below are congruent? Justify your answer.

    

24. Writing Anita says that you can rewrite any proof that uses the AAS Theorem as a proof that uses the ASA Postulate. Do you agree with Anita? Explain.
25. Proof Given: A E ¯ ║ B D ¯ , A E ¯ ≅ B D ¯ , eh e bar , box drawings double vertical . b d bar , comma . eh e bar , approximately equal to . b d bar , comma

    ∠ E ≅ ∠ D angle e approximately equal to , angle cap d

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

26. Proof Given: ∠ 1 ≅ ∠ 2 , angle 1 approximately equal to angle 2 comma  and D H ¯ d h bar  bisects ∠ B D F . angle b d f .

    Prove: Δ B D H ≅ Δ F D H cap delta b d h approximately equal to cap delta f d h

    

27. Draw a Diagram Draw two noncongruent triangles that have two pairs of congruent angles and one pair of congruent sides.
28. Proof Given: A B ¯ ║ D C ¯ , A D ¯ ║ B C ¯ eh b bar , box drawings double vertical . d c bar , comma . eh d bar , box drawings double vertical , b c bar

    Prove: Δ A B C ≅ Δ C D A cap delta eh b c approximately equal to cap delta c d eh

    

C Challenge

29. Given A D ¯ ║ B C ¯ eh d bar , box drawings double vertical , b c bar  and A B ¯ ║ D C ¯ , eh b bar , box drawings double vertical . d c bar , comma  name as many pairs of congruent triangles as you can.

    

30. Constructions In Δ R S T cap delta r s t  below, R S = 5 , R T = 9 , r s , equals 5 comma r t , equals 9 comma  and m ∠ T = 30 . m angle . t equals 30 .  Show that there is no SSA congruence rule by constructing Δ U V W cap delta u v w  with U V = R S ,  UW  = R T , u v equals r s comma , cap ucap w , equals r t comma  and m ∠ W = m ∠ T , m angle , w equals . m angle t comma  but with Δ U V W ≇ Δ R S T . cap delta u v w neither approximately nor actually equal to cap delta r s t .

    

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