Name: ___________________________________
Date: _________________
PROVING PARALLELOGRAMS USING COORDINATE GEOMETRY
GEOMETRY N
Recall: We define a parallelogram as a quadrilateral with two pairs of parallel sides.
Example: Quadrilateral ABCD has vertices A(2, 5), B(3, 2), C(-1, -1) and D(-2, 2). Prove using coordinate
geometry that ABCD is a parallelogram.
Step 1: Plot the quadrilateral on graph paper.
y
Step 2: Calculate the slope of each line segment.
AB:
x
BC:
CD:
DA:
Step 3: Determine which sides are parallel and state why.
Step 4: Write a conclusion.
GEOMETRY- UNIT #4 – COORDINATE GEOMETRY– LESSON #6
1. Quadrilateral ABCD has vertices A(3, 1), B(-1, -1), C(-6, 2) and D(-2, 4). Prove using coordinate geometry
that ABCD is a parallelogram.
Step 1: Plot the quadrilateral on the axes shown below.
y
Step 2: Calculate the slopes of each line segment.
AB:
x
BC:
CD:
DA:
Step 3: Determine which sides are parallel and state why.
Step 4: Write a conclusion.
2.
GEOMETRY- UNIT #4– COORDINATE GEOMETRY– LESSON #6
Quadrilateral PQRS has vertices P(5, 2), Q(2, -2), R(-3, -2) and S(0, 2). Prove using coordinate geometry
that PQRS is a parallelogram.
y
x
3. Quadrilateral WXYZ has vertices W(1, 5), X(6, 0), Y(3, -3) and Z(-2, 2). Prove using coordinate geometry
that WXYZ is a parallelogram.
y
x
4.
GEOMETRY- UNIT #4– COORDINATE GEOMETRY– LESSON #6
Carla thinks that ABCD, which has vertices of A(1, 4), B(4, 1), C(-1, -2), and D(-5, 0), is a parallelogram.
Prove using coordinate geometry that Carla is wrong.
y
x
5. Quadrilateral PQRS has vertices P(5, 2), Q(2, -2), R(-2, -2) and S(-3, 2). Prove using coordinate geometry
that PQRS is not a parallelogram.
y
x
Question: Although PQRS is not a parallelogram, it is a special type of quadrilateral. What is its name? {You
will need to think back to previous math courses}
GEOMETRY- UNIT #4– COORDINATE GEOMETRY– LESSON #6
6. Quadrilateral DEFG has vertices D(2, 4), E (3,5), F (3, 2), and G(2, 3). Prove using coordinate
geometry that DEFG is a parallelogram.
y
x
7. Quadrilateral WXYZ has vertices W(-3,2), X(1,4), Y(-2,0) and Z(-5,-2). Prove using coordinate geometry
that WXYZ is not parallelogram.
y
x
GEOMETRY- UNIT #4– COORDINATE GEOMETRY– LESSON #6