CC Geometry H
Aim #16: How do we apply the properties of quadrilaterals in coordinate
geometry proofs (day 2)?
Do Now: Prove that the figure below is a rectangle, but NOT a square. There are
many ways to do this. Choose one of the methods below.
Choice 1: Show it‛s a parallelogram with one right
angle and 2 consecutive sides that are not equal.
A
B
D
C
Choice 2: Show that the diagonals bisect each other and are equal and that two
consecutive sides are not equal.
Choice 3: Show that the quadrilateral has 4 right angles and that the diagonals
are not perpendicular.
1) Consider the quadrilateral with vertices A(-2,-1), B(2,2), C(5,-2) and D(1,-5).
a) Prove that the quadrilateral is a rectangle.
b) Prove if the quadrilateral is a square? Justify.
c) What is the area of the quadrilateral?
d) What is the area of the region of the quadrilateral that lies to the right of the
y-axis?
e) What is the equation of the perpendicular bisector of the side of the
quadrilateral that lies in the fourth quadrant?
2) The vertices of ΔGHI are G(1,1), H(5,3) and I(4,5). Prove that ΔGHI is a right
triangle. State the coordinates of point J such that quadrilateral GHIJ is a
rectangle. Prove that GHIJ is a rectangle.
3) Prove that the quadrilateral with vertices K(3,2), L(7,0), M(11,2) and N(7,4) is a
rhombus and not a square.
Name: ____________________
CC Geometry H
Date: ___________
HW #16
1) Prove that the quadrilateral with coordinates P(1,1), Q(2,4), R(5,6) and S(4,3) is
a parallelogram.
2) Prove that the quadrilateral with coordinates C(0,0), O(5,0), A(5,2) and T(0,2)
is a rectangle.
3) Draw quadrilateral MNPQ if M(1,7), N(-2,2), P(3,-1) and Q(6,4).
a) Find the slopes of MN and NP.
What can you conclude about ≮MNP?
b) What is the best name for MNPQ?
Justify your answer.
c) Which diagonal is longer? Explain how you know your answer is correct.
d) Find the midpoint of MN.
Mixed Review:
0
1) A robot begins at position (-80,45) and moves on a path to (100,-60). It turns 90
counterclockwise.
a) What point with y-coordinate 120 is on this path?
b) Write an equation of the line after the turn.
c) If it stops to charge on the x-axis, what is the location of the charger?
2) What is the equation of the line that is the perpendicular bisector of the
segment that connects A(1,3) and B(5,12)?
3) Examine the diagram below.
a) Are the triangles in the diagram similar? Justify your answer using similarity
transformations.
b) What is the relationship between the lengths of HR and AK? Between the
lengths of SH and SA? Between the lengths of SH and HA?
c) If SK = 20 units and RH = 8 units, what is HA?
Attachments
Triangle Coor HW Answer Key.pdf