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CC Coordinate Algebra
Unit 6 – Connecting Algebra and Geometry Though Coordinates
Proving Quadrilaterals
Quadrilateral ABCD has the vertices: A(8, 7), B(12, 4), C(5, -2), D(1, 1)
Definition: A parallelogram is a quadrilateral with two pairs of opposite sides that parallel.
1. What formula do we use to show sides are parallel?
2. Plot and label the figure. Name 2 pairs of opposite sides.
3. Show with mathematical calculations that these opposite sides
are parallel to prove ABCD is a parallelogram.
Parallelogram EFGH has vertices: E(-12, -4), F(-4, 4), G(-7, 7), H(-15, -1)
Theorem – Both pairs of opposite sides in a parallelogram are congruent.
4. What formula do we use to show sides are congruent?
5. Plot and label the figure. Name 2 pairs of opposite sides.
6. Show with mathematical calculations that these opposite sides
are congruent to prove EFGH is a parallelogram.
7. Calculate the perimeter of Parallelogram EFGH.
8. Calculate the area of Parallelogram EFGH.
CC Coordinate Algebra
Unit 6 – Connecting Algebra and Geometry Though Coordinates
Rectangle EFGH has vertices: E(-12, -4), F(-4, 4), G(-7, 7), H(-15, -1)
Theorem – Both diagonals in a rectangle are congruent.
9. What formula do we use to show sides are congruent?
10. Plot and label the figure. Name 1 pair of diagonals.
11. Show with mathematical calculations that these diagonals
are congruent to prove EFGH is a rectangle.
Rectangle EFGH has vertices: E(-12, -4), F(-4, 4), G(-7, 7), H(-15, -1)
Theorem – A rectangle has 4 right angles.
12. What kind of lines make right angles? What formula do we use to
show these types of lines?
13. Plot and label the figure. Name all four sides.
14. Show with mathematical calculations that adjacent sides
make right angles to prove EFGH is a rectangle.
Rhombus JKLM has vertices: J(25, 14), K(15, 14), L(7, 8), M(17, 8)
Theorem – The diagonals in a rhombus are perpendicular.
15. What formula do we use to prove perpendicular lines?
16. Plot and label the figure. Name the two diagonals.
17. Show with mathematical calculations that the diagonals are
perpendicular to prove JKLM is a Rhombus.