26. 1. Coordinate Geometry Graph the points A ( − 5 , 6 ) , B ( 1 , 3 ) , D ( − 8 , 0 ) , eh open negative 5 comma 6 close comma b open 1 comma 3 close comma d open negative 8 comma 0 close comma  and E ( − 2 , − 3 ) . e open negative 2 comma negative 3 close .  Draw A B ¯ , A E ¯ , B D ¯ , eh b bar , comma . eh e bar , comma . b d bar , comma  and D E ¯ . d e bar , .  Label point C, the intersection of A E ¯ eh e bar  and B D ¯ . b d bar , .
    2. Find the slopes of A E ¯ eh e bar  and B D ¯ . b d bar , .  How would you describe ∠ A C B angle eh c b  and ∠ E C D ? angle e c d question mark
    3. Algebra Write equations for A E ↔ modified eh e with left right arrow above  and B D ↔ . modified b d with left right arrow above , .  What are the coordinates of C ? c question mark
    4. Use the Distance Formula to find AB, BC, DC, and D.
    5. Write a paragraph to prove that Δ A B C ≅ Δ E D C . cap delta eh b c approximately equal to cap delta e d c .

C Challenge

Geometry in 3 Dimensions For Exercises 27 and 28, use the figure below.

27. Proof Given: B E ¯ ⊥ E A ¯ , B E ¯ ⊥ E C ¯ , Δ A B C b e bar , up tack . e eh bar , comma . b e bar , up tack . e c bar , comma . cap delta eh b c  is equilateral

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

28. Given: Δ A E B ≅ Δ C E B ,  B E ¯ ⊥ E A ¯ , B E ¯ ⊥ E C ¯ cap delta eh e b approximately equal to cap delta c e b comma , b e bar , up tack . e eh bar , comma . b e bar , up tack , e c bar  Can you prove that Δ A B C cap delta eh b c  is equilateral? Explain.

Standardized Test Prep

SAT/ACT

29. You often walk your dog around the neighborhood. Based on the diagram below, which of the following statements about distances is true?

    

    1. S H = L H s h equals l h
    2. P H = C H p h equals c h
    3. S H > L H s h greater than l h
    4. P H < C H p h less than c h
30. What is the midpoint of L M ¯ l m bar  with endpoints L ( 2 , 7 ) l open 2 comma 7 close  and M ( 5 , − 1 ) ? m open 5 comma negative 1 close question mark
    6. (3.5, 3)
    7. (3.5, 4)
    8. (2, 4.5)
    9. (7, 6)

31. Short Response In equilateral Δ X Y Z , cap delta x y z comma  name four pairs of congruent right triangles. Explain why they are congruent.

    

Mixed Review

See Lesson 4-5.

For Exercises 32 and 33, what type of triangle must Δ S T U cap delta s t u  be? Explain.

32. Δ S T U ≅ Δ U T S cap delta s t u approximately equal to cap delta u t s
33. Δ S T U ≅ Δ U S T cap delta s t u approximately equal to cap delta u s t

Get Ready! To prepare for Lesson 4-7, do Exercises 34−36.

See Lessons 4-3 and 4-6.

Can you conclude that the triangles are congruent? Explain.

34. Δ A B C cap delta eh b c  and Δ L M N cap delta l m n
35. Δ L M N cap delta l m n  and Δ H J K cap delta h j k
36. Δ R S T cap delta r s t  and Δ A B C cap delta eh b c

    
    Image Long Description

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