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Exam 5: Quadrilaterals

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Question 31

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Given kite ABCD with and , the diagonals (if drawn)would be perpendicular. For diagonals and , what other relationship exists?

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Question 32

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If in , then is an altitude of with respect to base .

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Question 33

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For , is an altitude with respect to base . In relation to , what word is used for the length of ?

For a trapezoid, the lengths of the two bases are a and b. What expression represents the length of the median of the trapezoid?

In , M is the midpoint of and N is the midpoint of . If the length of is represented by , what expression (containing x )represents the length of ?

For a quadrilateral to be "cyclic," what requirement must be satisfied?

If and in quadrilateral ABCD , then ABCD is an isosceles trapezoid.

In isosceles trapezoid HJKL , . Suppose that points M , N , P , and Q are the midpoints of the sides , , , and respectively. If the length of diagonal is 10 cm, find the perimeter of MNPQ .

In , RS = 19, ST = 15, and WT = 10. Find the length of altitude .

The diagonals of any rhombus are perpendicular.

In rectangle ABCD , AB = 5 and BC = 4. As a square root, find the length of diagonal .

In isosceles trapezoid HJKL , . If and , find an expression for the perimeter of trapezoid HJKL .

Given trapezoid RSTV with median , find the length of if RS = 12.7 inches and VT = 17.5 inches.

The diagonals of any rhombus are perpendicular.

In quadrilateral WXYZ , . If and , determine a value of x so that WXYZ must be a parallelogram.

For a parallelogram to be a rhombus, what condition must it satisfy?

Both pairs of opposite sides of quadrilateral WXYZ are congruent. Being as specific as possible, what type of quadrilateral is WXYZ?

For trapezoid RSTV , . Also, M and N are the midpoints of the nonparallel sides as shown. In relation to trapezoid RSTV , what name is used for ?

For , points M , N , and P are the midpoints of the sides. If the perimeter of is 47 inches, find the perimeter of .

If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28.