Trapezoids and Kites

Question 1

Mary thinks the triangle is equilateral. How would you support or dispute her conjecture?

Revolt · Accepted Answer

Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.

Question 2

Question 2

Revolt · Accepted Answer

–1

Question 3

Question 3

Revolt · Accepted Answer

negative reciprocals

Question 4

Question 4

Revolt · Accepted Answer

perpendicular

Question 5

Question 5

Revolt · Accepted Answer

perpendicular and share the same midpoint

Question 6

Triangle ABC is an isosceles triangle in which sideAB = AC. What is the perimeter of triangle ABC?

Revolt · Accepted Answer

10 + units

Question 7

Which steps will verify that a parallelogram is a rectangle? Check all that apply.Calculate the lengths of the diagonals, and show that they are equal.Calculate the lengths of all sides, and show that both pairs of opposite sides are congruent.Calculate the slope of each diagonal, and show that the lines are perpendicular.Calculate the midpoints of each diagonal, and show the diagonals bisect each other.Calculate the slopes of every side, and show that adjacent sides are perpendicular.

Revolt · Accepted Answer

Calculate the lengths of the diagonals, and show that they are equal.; Calculate the slopes of every side, and show that adjacent sides are perpendicular.

Question 8

Prove that the diagonals of kite UVWX are perpendicular. Step 1: Determine the slope of XV. The slope of XV is . Step 2: Determine the slope of UW. The slope of UW is . Step 3: The slopes of the diagonals are . The diagonals of kite UVWX are .

Revolt · Accepted Answer

1; Selection 1: 1; Selection 2: –1; Selection 3: negative reciprocals; Selection 4: perpendicular

Question 9

Prove the diagonals of the square with vertices P(0, 4), Q(4, 4), R(0, 0), and S(4, 0) are perpendicular bisectors of each other. Step 1: Calculate the slope of the diagonals. The slope of diagonal PS is . The slope of diagonal QR is . Step 2: Calculate the midpoint of the diagonals. The midpoint of PS is . The midpoint of QR is . The diagonals of the square are perpendicular bisectors because the diagonals are .

Revolt · Accepted Answer

–1; Selection 1: –1; Selection 2: 1; Selection 3: (2, 2); Selection 4: (2, 2); Selection 5: perpendicular and share the same midpoint

Question 10

Which statement proves that quadrilateral HIJK is a kite?

Revolt · Accepted Answer

IH = IJ = 3 and JK = HK = , and IH ≠ JK and IJ ≠ HK.

Trapezoids and Kites Answers

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