AnswersOC27 GEO-1206310-S2-Degele-VOL7006PArea of Triangles and Parallelograms

Figures in the Coordinate Plane Answers

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

A
Calculate the slope of all three sides, and check whether the slopes are equal.
B
Calculate the slope of all three sides, and check whether any slopes are reciprocals.
C
Use the distance formula to calculate the length of all three sides, and check whether all sides are congruent.
D
Use the distance formula to calculate the length of all three sides, and check whether any two sides are congruent.
3

equalnegative reciprocalsreciprocals

A
equal
B
negative reciprocals
C
reciprocals
4

congruentparallelperpendicular

A
congruent
B
parallel
C
perpendicular
115774

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.

Answers:
The slope of diagonal QR is .:1
The midpoint of PS is .:(2, 2)
The midpoint of QR is .:(2, 2)
The diagonals of the square are perpendicular bisectors because the diagonals are .:perpendicular and share the same midpoint
115775

–101

A
–1
B
0
C
1
115776

(0, 4) (2, 2)(4, 2)

A
(0, 4)
B
(2, 2)
C
(4, 2)
115777

(4, 0)(2, 2)(2, 4)

A
(4, 0)
B
(2, 2)
C
(2, 4)
115778

parallel and share the same midpointperpendicular and share the same midpointthe same length

A
parallel and share the same midpoint
B
perpendicular and share the same midpoint
C
the same length
115779

23364665

A
23
B
36
C
46
D
65
115781

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.

A
Calculate the lengths of the diagonals, and show that they are equal.
B
Calculate the lengths of all sides, and show that both pairs of opposite sides are congruent.
C
Calculate the slope of each diagonal, and show that the lines are perpendicular.
D
Calculate the midpoints of each diagonal, and show the diagonals bisect each other.
E
Calculate the slopes of every side, and show that adjacent sides are perpendicular.
115782

–101

A
–1
B
0
C
1
115783

Which statement proves that quadrilateral HIJK is a kite?

A
HI ⊥ IJ, and m∠H = m∠J.
B
IH = IJ = 3 and JK = HK = , and IH ≠ JK and IJ ≠ HK.
C
IK intersects HJ at the midpoint of HJ at (−1.5, 2.5).
D
The slope of HK = and the slope of JK = .
115784

–10undefined

A
–1
B
0
C
undefined

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