1. Alan claims that quadrilateral JKLM is a rhombus. Its vertices are J(0, 0), K(7, 2), L(11, 8), and M(4, 6).
a) Draw JKLM on graph paper and measure each side as best you can with a ruler. What is the
measurement of each side?
JK: ________________ KL: _______________ LM: _________________ MJ: __________________
b) Do the measurements indicate that JKLM is a rhombus? Explain
c) Use the distance formula to find the exact length of each of the sides. Do you think that JKLM is a
rhombus? Why or why not?
d) Explain how you could find out if JKLM is a parallelogram. Is JKLM a parallelogram? Prove your
answer.
e) Look back at parts (b) and (c). Why do you suppose mathematicians prefer to verify information using
formulas instead of measurements or drawings?
2.
Quadrilateral ABCD has vertices A(4, 1), B(1, -1), C(-2, 1), and D(1, 3)
a) Draw the quadrilateral ABCD on graph paper
b) Find the length of each side of quadrilateral ABCD
c) Find the slope of each side of ABCD
d) What type of quadrilateral is ABCD? Be as specific as possible!
e) Find the perimeter of ABCD.
1. Alan claims that quadrilateral JKLM is a rhombus. Its vertices are J(0, 0), K(7, 2), L(11, 8), and M(4, 6).
a) Draw JKLM on graph paper and measure each side as best you can with a ruler. What is the
measurement of each side?
JK: ________________ KL: _______________ LM: _________________ MJ: __________________
b) Do the measurements indicate that JKLM is a rhombus? Explain
c) Use the distance formula to find the exact length of each of the sides. Do you think that JKLM is a
rhombus? Why or why not?
d) Explain how you could find out if JKLM is a parallelogram. Is JKLM a parallelogram? Prove your
answer.
e) Look back at parts (b) and (c). Why do you suppose mathematicians prefer to verify information using
formulas instead of measurements or drawings?
f)
Quadrilateral ABCD has vertices A(4, 1), B(1, -1), C(-2, 1), and D(1, 3)
a) Draw the quadrilateral ABCD on graph paper
b) Find the length of each side of quadrilateral ABCD
c) Find the slope of each side of ABCD
d) What type of quadrilateral is ABCD? Be as specific as possible!
e) Find the perimeter of ABCD.