22. Sierpinski's Triangle Sierpinski's triangle is a famous geometric pattern. To draw Sierpinski's triangle, start with a single triangle and connect the midpoints of the sides to draw a smaller triangle. If you repeat this pattern over and over, you will form a figure like the one shown. This particular figure started with an isosceles triangle. Are the triangles outlined in red congruent? Explain.

    

23. Constructions Use a straightedge to draw any triangle JKL. Then construct Δ M N P ≅ Δ J K L cap delta m n p approximately equal to cap delta j k l  using the given postulate.
    1. SSS
    2. SAS

Can you prove the triangles congruent? If so, write the congruence statement and name the postulate you would use. If not, write not enough information and tell what other information you would need.

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25. 
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27. Reasoning Suppose G H ¯ ≅ J K ¯ , H I ¯ ≅ K L ¯ , g h bar , approximately equal to . j k bar , comma . h i bar , approximately equal to . k l bar , comma  and ∠ I ≅ ∠ L . angle i approximately equal to . angle l .  Is Δ G H I cap delta g h i  congruent to Δ J K L . cap delta j k l .  Explain.
28. Proof Given: G K ¯ g k bar  bisects ∠ J G M , G J ¯ ≅ G M ¯ angle j g m comma . g j bar , approximately equal to . g m bar

    Prove: Δ G J K ≅ Δ G M K cap delta g j k approximately equal to cap delta g m k

    

29. Proof Given: A E ¯ eh e bar  and B D ¯ b d bar  bisect each other.

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

    

30. Proof Given: F G ¯ ║ K L ¯ , F G ¯ ≅ K L ¯ f g bar , box drawings double vertical . k l bar , comma . f g bar , approximately equal to . k l bar

    Prove: Δ F G K ≅ Δ K L F cap delta f g k approximately equal to cap delta k l f

    

31. Proof Given: A B ¯ ⊥ C M ¯ , A B ¯ ⊥ D B ¯ , C M ¯ ≅ D B ¯ , eh b bar , up tack . c m bar , comma . eh b bar , up tack . d b bar , comma . c m bar , approximately equal to . d b bar , comma

    M is the midpoint of A B ¯ eh b bar

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

    

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