Algebra Find the value of x.

See Problem 3.

25. Surveying A surveyor needs to measure the distance PQ across the lake. Beginning at point S, she locates the midpoints of S Q ¯ s q bar  and S P ¯ s p bar  at M and N. She then measures N M ¯ . n m bar , .  What is PQ?

    

B Apply

26. Kayaking You want to paddle your kayak across a lake. To determine how far you must paddle, you pace out a triangle, counting the number of strides, as shown.
    1. If your strides average 3.5 ft, what is the length of the longest side of the triangle?
    2. What distance must you paddle across the lake?

    

27. Architecture The triangular face of the Rock and Roll Hall of Fame in Cleveland, Ohio, is isosceles. The length of the base is 229 ft 6 in. Each leg is divided into four congruents parts by the red segments. What is the length of the white segment? Explain your reasoning.

    

28. Think About a Plan Draw Δ A B C . cap delta eh b c .  Construct another triangle so that the three sides of Δ A B C cap delta eh b c  are the midsegments of the new triangle.
    • Can you visualize or sketch the final figure?
    • Which segments in your final construction will be parallel?
29. Writing In the figure below, m ∠ Q S T = 40 . m angle q s t , equals 40 , .  What is m ∠ Q P R ? m angle q p r question mark  Explain how you know.
30. Coordinate Geometry The coordinates of the vertices of a triangle are E(1, 2), F(5, 6), and G ( 3 , − 2 ) . g open 3 comma negative 2 close .

    

    1. Find the coordinates of H, the midpoint of E G ¯ , e g bar , comma  and J, the midpoint of F G ¯ . f g bar , .
    2. Show that H J ¯ ║ E F ¯ . h j bar , box drawings double vertical . e f bar , .
    3. Show that H J = 1 2 E F . h j equals . 1 half e f .

X is the midpoint of U V ¯ . u v bar , .   Y is the midpoint of U W ¯ . u w bar , .

31. If m ∠ U X Y = 60 , m angle u x y , equals 60 , comma  find m ∠ V . m angle v .
32. If m ∠ W = 45 , m angle , w equals 45 , comma  find m ∠ U Y X . m angle u y x .
33. If X Y = 50 , x y equals 50 . comma  find VW.
34. If V W = 110 , v w equals 110 . comma  find XY.

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