Analytic Proofs Final Project
Analytic Proofs
Now that we have completed the first chapter, you will have a chance to show what you
have learned. The class will complete a number of group projects requiring the use of the
skills we have been working on the past few weeks. Keeping in mind that geometric
proofs require lots of practice, this project will involve analytic proofs. Each group of
four or five will be given one problem to prove.
Successful completion of this project includes:
o A detailed, accurate drawing of the figure with all points labeled
o A clear explanation of the problem and the steps needed to prove the
statement
o Detailed and systematic solving of all necessary equations
o Written explanation of the problem and the proof, in complete,
grammatically correct sentences
o Any additional geometric information that can be inferred from the
information
o A verbal explanation by the group about the problem and all work
completed
o Working successfully as a team to solve the problem
Grading will be based on the attached rubric.
1)
The vertices of quadrilateral JOHN are J(-3, 1), O(3, 3), H(5, 7), and N(-1, 5).
Use coordinate geometry to prove that quadrilateral JOHN is a parallelogram.
2)
Quadrilateral MIKE has vertices M(4, 1), I(6, 4), K(12, 0), E(10, -3). Use
coordinate geometry to prove that quadrilateral MIKE is a rectangle.
3)
The coordinates of the vertices of quadrilateral DIAN are D(0, 5), I(3, 6), A(4, 3),
and N(1, 2). Use coordinate geometry to prove that quadrilateral DIAN is a square.
4)
Quadrilateral NORA has vertices N(3, 2), O(7, 0), R(11, 2), and A(7, 4). Use
coordinate geometry to prove that NORA is a rhombus, but not a square.
5)
The vertices of quadrilateral KAIT are K(0, 0), A(a, 0), I(a+b, c), and T(b, c).
Use coordinate geometry to prove that quadrilateral KAIT is a parallelogram.
6)
Quadrilateral JACK has vertices J(1, -4), A(10, 2), C(8, 5), and K(2, 1). Use
coordinate geometry to prove that JACK is a trapezoid, but is not isosceles.
7)
The vertices of quadrilateral MARY are M(-3, 3), A(7, 3), R(3, 6), and Y(1, 6).
Use coordinate geometry to prove that quadrilateral MARY is an isosceles trapezoid.