Download Mod 4 - Aim #15 - Manhasset Public Schools

CC Geometry H
Aim #15: How do we apply the properties of quadrilaterals in coordinate
geometry proofs?
Do Now: ΔAFN: A(-7,6), F(-1,6), N(-4,2). Prove the triangle is isosceles, but not
equilateral. Use of graph is optional. Label your work and write a concluding
statement.
1) One method to prove a quadrilateral is a parallelogram is to prove the diagonals
bisect each other: Show that the diagonals have the same midpoint. Write a
concluding statement.
2) Given a quadrilateral with vertices E(0,5), F(6,5), G(4,0) and H(-2,0).
a) Prove that EFGH is a parallelogram by showing that both pairs of opposite sides
are parallel (a second method). Use of the grid is optional. Write a concluding
statement.
b) Prove (2,2.5) is the intersection point of both diagonals of this quadrilateral.
3) Given quadrilateral JKLM with vertices J(-4,2), K(1,5), L(4,0) and M(-1,-3).
a) Is it a trapezoid? Prove. (If at least one pair of opposite sides is parallel, then
it is a trapezoid.)
b) Is it a parallelogram? Prove.
c) Is it a rectangle? Prove.
d) Is it a rhombus? Prove.
e) Is it a square? Explain.
f) Name a point on a diagonal of JKLM. Explain how you know.
4) The points O(0,0), A(-4,1), B(-3,5) and C(1,4) are the vertices of parallelogram
OABC. Is this parallelogram a rectangle? Prove and write a concluding statement.
Use of grid is optional.
5) A quadrilateral has vertices
,
,
, and
.
Prove that the quadrilateral is a rectangle. Write a concluding statement.
A guide to proving different types of quadrilaterals using coordinate geometry:
3. Prove a quadrilateral with 4 rt. angles. Slope formula 4 times.
Option 4:
1. All 4 angles are equal (proving
parallelogram and rectangle)
2. Diagonals are perpendicular.
1. Slope formula 4 times.
2. Slope formula 2 twice.
Name: ____________________
Date: _________________
CC Geometry H
HW #15
1) Complete:
a) Parallel line have ________________________ slopes.
b) Perpendicular lines, which form _____________ angles have
_______________ __________________ slopes.
c) Congruent segments have ______________ __________________.
d) Segments that bisect each other share the same _________________.
2) Given a quadrilateral with vertices A(-1,3), B(1,5), C(5,1) and D(3,-1).
a) Prove that ABCD is a rectangle.
[Use of the grid is optional.]
b) Prove that (2,2) is a point on both diagonals of the quadrilateral.
3) Prove that the quadrilateral with the vertices A(-1,4), B(2,6), (C5,4) and D(2,2) is
a rhombus.
4) Prove that the quadrilateral with the vertices A(0,0), B(4,3), C(7,-1) and D(3,-4)
is a square.
Mixed Review:
1) In rhombus ABCD, the coordinates of the endpoints of the diagonal AC are
A(-3,-2) and C(5,4). Write an equation of the line that contains diagonal BD. Using
the given information, explain how you know that your line contains diagonal BD.
[Use of the grid is optional.]
2) Given: Quad. TREK
≮1 is supp. to ≮4
≮RED ≅ ≮4
Prove: parallelogram FRED
statements
reasons
Attachments
Triangle Coor HW Answer Key.pdf