20. Clothing Design The figure below is part of a clothing design pattern, and it has the following relationships.

    
    Image Long Description

    • G C ¯ ⊥ A C ¯ g c bar , up tack , eh c bar
    • A B ¯ ⊥ B C ¯ eh b bar , up tack , b c bar
    • A B ¯ | | D E ¯ | | F G ¯ eh b bar , vertical line vertical line , d e bar , vertical line vertical line , f g bar
    • m ∠ A = 50 m angle . eh equals 50
    • Δ D E C cap delta d e c  is isosceles with base D C ¯ . d c bar , .
    1. Find the measures of all the numbered angles in the figure.
    2. Suppose A B ¯ ≅ F C ¯ . eh b bar , approximately equal to . f c bar , .  Name two congruent triangles and explain how you can prove them congruent.
21. Proof Given: A C ¯ ≅ E C ¯ , C B ¯ ≅ C D ¯ eh c bar , approximately equal to . e c bar , comma . c b bar , approximately equal to . c d bar

    Prove: ∠ A ≅ ∠ E angle eh approximately equal to angle e

    

22. Proof Given: Q T ¯ ⊥ P R ¯ , Q T ¯ q t bar , up tack . p r bar , comma . q t bar  bisects P R ¯ , Q T ¯ p r bar , comma . q t bar  bisects ∠ V Q S angle v q s

    Prove: V Q ¯ ≅ S Q ¯ v q bar , approximately equal to . s q bar

    

Open-Ended Draw the diagram described.

23. Draw a vertical segment on your paper. On the right side of the segment draw two triangles that share the vertical segment as a common side.
24. Draw two triangles that have a common angle.
25. Proof Given: T E ¯ ≅ R I ¯ , T I ¯ ≅ R E ¯ , ∠ T D I t e bar , approximately equal to . r i bar , comma . t i bar , approximately equal to . r e bar , comma . angle t d i  and ∠ R O E angle r o e  are right

    Prove: T D ¯ ≅ R O ¯ t d bar , approximately equal to . r o bar

    

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

    Prove: A E ¯ ≅ D E ¯ eh e bar , approximately equal to . d e bar

    

C Challenge

27. Reasoning Draw a quadrilateral ABCD with A B ¯ | | D C ¯ , A D ¯ | | B C ¯ , eh b bar , vertical line vertical line . d c bar , comma . eh d bar , vertical line vertical line . b c bar , comma  and diagonals A C ¯ eh c bar  and D B ¯ d b bar  intersecting at E. Label your diagram to indicate the parallel sides.
    1. List all the pairs of congruent segments in your diagram.
    2. Writing Explain how you know that the segments you listed are congruent.

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