Quadrilaterals and Coordinates Proof Coordinate Proof for Parallelograms Opening routine Determine if the following quadrilateral is a parallelogram for the given values of the variables. x = 6 y = 3.5

Topic IV: Quadrilaterals and Coordinate Proof

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Objective: Use coordinate geometry to prove that a quadrilateral is parallelogram. Essential Question: What criteria can be used in a coordinate proof to determine of a quadrilateral is a parallelogram?

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Vocabulary Parallelogram: Is a quadrilateral with two pairs of parallel sides. Rectangle: Is a quadrilateral with four right angles. Rhombus: Is a simple quadrilateral whose four sides all have the same length. Square: A square is a regular quadrilateral, which means that it has four equal sides and four equal angles.

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Vocabulary Trapezoid: Is a quadrilateral that has a pair of opposite sides parallel. The sides that are parallel are called “bases”. Isosceles trapezoid: Is a special type of trapezoid in which non-parallel sides and base angles are equal. Kite: Is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms To prove if a quadrilateral in the coordinate plane is a parallelogram, it can be used four different criteria: Distance formula to determine if both opposite sides are congruent. Slope formula to determine if both opposite sides are parallel. Midpoint formula to determine if the diagonals bisect each other. Distance formula and slope formula to determine if one pair of opposite sides is both parallel and congruent.

Quadrilaterals and Coordinates Proof Test for Parallelogram in the Coordinate Plane Guided Practice – WE DO

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Guided Practice – WE DO The vertices of quadrilateral JOHN are J (3, 1), O (3, 3), H (5, 7) and N (1, 5). Use the coordinate geometry to prove that quadrilateral JOHN is a parallelogram.

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Guided Practice – WE DO

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Guided Practice – WE DO We will use the distance formula and the slope formula to determine if the quadrilateral is a parallelogram.

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Guided Practice – WE DO Determine whether the figure with the given vertices is a parallelogram, P (5,3), Q (1,5), R (6,1), S (2,7)

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Guided Practice – WE DO Determine whether the figure with the given vertices is a parallelogram, P (5,3), Q (1,5), R (6,1), S (2,7) Then PQRS is a parallelogram

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Independent Practice - YOU DO Worksheet “Coordinates Proof for Parallelogram” Exercises from 1 to 4

Quadrilaterals and Coordinates Proof Coordinates Proof for Parallelograms Closure Essential Question: What criteria can be used in a coordinate proof to determine of a quadrilateral is a parallelogram?