I J ¯ i j bar  is a midsegment of Δ F G H . I J = 7 , F H = 10 ,  and  G H = 13 . cap delta f g h . i j equals 7 comma f h equals 10 comma , and g h equals 13 .  Find the perimeter of each triangle.

35. Δ I J H cap delta i j h
36. Δ F G H cap delta f g h

    

37. Kite Design You design a kite to look like the one below. Its diagonals measure 64 cm and 90 cm. You plan to use ribbon, represented by the purple rectangle, to connect the midpoints of its sides. How much ribbon do you need?

    

    1. 77 cm
    2. 122 cm
    3. 154 cm
    4. 308 cm

Algebra Find the value of each variable.

Use the figure below for Exercises 42–44.

42. D F = 24 , B C = 6 , d f equals 24 . comma , b c equals 6 , comma  and D B = 8 . d b equals 8 , .  Find the perimeter of Δ A D F . cap delta eh d f .
43. Algebra If B E = 2 x + 6 b e equals . 2 x plus 6  and D F = 5 x + 9 , d f equals . 5 x plus 9 , comma  find DF.
44. Algebra If E C = 3 x − 1 e c equals 3 x minus 1  and A D = 5 x + 7 , eh d equals . 5 x plus 7 , comma  find EC.
45. Open-Ended Explain how you could use the Triangle Midsegment Theorem as the basis for this construction: Draw C D ¯ . c d bar , .  Draw point A not on C D ¯ . c d bar , .  Construct A B ¯ eh b bar  so that A B ¯ ║ C D ¯ eh b bar , box drawings double vertical , c d bar  and A B = 1 2 C D . eh b equals . 1 half c d .

C Challenge

46. Reasoning In the diagram below, K, L, and M are the midpoints of the sides of Δ A B C . cap delta eh b c .  The vertices of the three small purple triangles are the midpoints of the sides of Δ K B L , Δ A K M , cap delta k b l comma cap delta eh k m comma  and Δ M L C . cap delta m l c .  The perimeter of Δ A B C cap delta eh b c  is 24 cm. What is the perimeter of the shaded region?

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