Find the measures of the numbered angles in each rhombus.

15. 
16. 
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17. 

See Problem 3.

Algebra LMNP is a rectangle. Find the value of x and the length of each diagonal.

18. L N = x  and  M P = 2 x − 4 l n equals x , and m p equals , 2 x minus 4
19. L N = 5 x − 8 l n equals , 5 x minus 8 and M P = 2 x + 1 m p equals , 2 x plus 1
20. LN = 3x + 1 and M P = 8 x − 4 m p equals , 8 x minus 4
21. L N = 9 x − 14 l n equals . 9 x minus 14 and M P = 7 x + 4 m p equals , 7 x plus 4
22. L N = 7 x − 2 l n equals , 7 x minus 2 and M P = 4 x + 3 m p equals , 4 x plus 3
23. L N = 3 x + 5 l n equals , 3 x plus 5 and M P = 9 x − 10 m p equals . 9 x minus 10

B Apply

Determine the most precise name for each quadrilateral.

List the quadrilaterals that have the given property. Choose among parallelogram, rhombus, rectangle, and square.

28. All sides are ≅ . approximately equal to .
29. Opposite sides are ≅ . approximately equal to .
30. Opposite sides are ∥ . parallel to .
31. Opposite are ≅ . approximately equal to .
32. All are right .
33. Consecutive are supplementary.
34. Diagonals bisect each other.
35. Diagonals are ≅ . approximately equal to .
36. Diagonals are ⊥ . up tack .
37. Each diagonal bisects opposite .

Algebra Find the values of the variables. Then find the side lengths.

38. rhombus

    

39. square

    

40. Proof Think About a Plan Write a proof.

    Given: Rectangle PLAN

    Prove: Δ L T P ≅ Δ N T A cap delta l t p approximately equal to cap delta n t eh

    

    • What do you know about the diagonals of rectangles?
    • Which triangle congruence postulate or theorem can you use?

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