Aim #11: How do we apply the properties of quadrilaterals in coordinate
CC Geometry R
geometry proofs (day 2)?
1) Quadrilateral ABCD has vertices A(-3,2), B(-1,5), C(5,1) and D(3,-2).
Prove that ABCD is a rectangle.
2) Quadrilateral ABCD has vertices A(1,4), B(4,0), C(0,-3) and D(-3,1).
Prove that ABCD is a square.
3) Quadrilateral PQRS has vertices P(2,1), Q(6,3), R(8,7) and S(4,5).
Prove that PQRS is a rhombus, but not a square.
4) Quadrilateral JAME has vertices J(2,-2), A(8,-1), M(9,3) and E(3,2).
a) Prove that JAME is a parallelogram.
b) Prove that JAME is a not a rectangle.
Name: ____________________
Date: ___________
CC Geometry R
HW #11
1. Quadrilateral ABCD is graphed on the set of axes below.
Which quadrilateral best classifies ABCD?
a) trapezoid
c) rhombus
b) rectangle
d) square
2. Which type of triangle can be drawn using the points (-2,3), (-2,-7), and (4,-5)?
a) scalene
b) isosceles
c) equilateral
d) no triangle can be drawn
3. The vertices of ∆ABC are A(-1,-2), B(-1,2) and C(6,0).
Which conclusion can be made about the angles of ∆ABC?
a)
b)
c)
d)
4) Given quadrilateral JKLM with vertices J(-4,2), K(1,5), L(4,0) and M(-1,-3).
a) Is it a trapezoid? Explain. (If one pair of opposite sides is parallel, then it is a
trapezoid.)
b) Is it a parallelogram? Explain.
c) Is it a rectangle? Explain.
d) Is it a rhombus? Explain.
e) Is it a square? Explain.
f) Name a point on the diagonal of JKLM. Explain how you know.
Name: ____________________
Date: ___________
CC Geometry R
HW #11
1. Quadrilateral ABCD is graphed on the set of axes below.
Which quadrilateral best classifies ABCD?
a) trapezoid
c) rhombus
b) rectangle
d) square
2. Which type of triangle can be drawn using the points (-2,3), (-2,-7), and (4,-5)?
a) scalene
b) isosceles
c) equilateral
d) no triangle can be drawn
3. The vertices of ∆ABC are A(-1,-2), B(-1,2) and C(6,0).
Which conclusion can be made about the angles of ∆ABC?
a)
b)
c)
d)
4) Given quadrilateral JKLM with vertices J(-4,2), K(1,5), L(4,0) and M(-1,-3).
a) Is it a trapezoid? Explain. (If one pair of opposite sides is parallel, then it is a
trapezoid.)
slope of JK = 3/5
slope of ML = 3/5
JK ll ML because the slopes are equal.
Yes, JKLM is a trapezoid because two sides are parallel.
K
J
L
b) Is it a parallelogram? Explain.
JK ll ML [proven in part (a)]
slope of JM = ­5/3
slope of LK = ­5/3
M
Yes, JKLM is a parallelogram because both pairs of opposite sides are parallel.
c) Is it a rectangle? Explain.
The slopes of JM and JK are opposite reciprocals.
Therefore, JM JK.
≮J is a right angle.
Yes, JKLM is a rectangle because a parallelogram with a right angle is a rhombus. d) Is it a rhombus? Explain.
JM = √34
JK = √34
Yes, JKLM is a rhombus because a parallelogram with 2 equal adjacent sides is a rhombus.
e) Is it a square? Explain.
Yes, JKLM is a square because...
a rhombus with a right angle is a square.
OR
a rectangle with 2 equal adjacent sides is a square.
f) Name a point on the diagonals of JKLM. Explain how you know.
(0,1), the midpoint of the diagonals The diagonals of a parallelogram bisect each other.
The intersection of the diagonals is the midpoint of each diagonal.