Coordinate geometry proofs

Emma and Rena are planning to meet at a park. Emma is at point A and Rena is at point B on a map. What formula do they use to find the length of the path between them?

• Midpoint Formula

• Slope Formula

• Pythagorean Theorem

• Distance Formula

Orly and Rena are designing a new bike path and need to ensure that two sections of the path are parallel. Which formula should they use to prove the sections are parallel or perpendicular?

• Distance Formula

• Slope Formula

• Midpoint Formula

• Pythagorean Theorem

Nili and Eliana are planning to build a rectangular garden in their backyard. How can they prove that the shape they have marked out is a parallelogram?

• Both pairs of opposite sides are congruent

• Diagonals are congruent

• One pair of opposite sides are congruent 

• Both pairs of opposite sides are congruent and diagonals are congruent

Annabelle and Orly are helping their teacher to arrange the classroom. They have a large rectangular bulletin board and want to make sure it's a perfect rectangle. How can they prove the bulletin board is a Rectangle?

• Both pairs of opposite sides are congruent

• Diagonals are congruent

• One pair of opposite sides are congruent 

• Both pairs of opposite sides are congruent and diagonals are congruent

Aden is designing a square garden and wants to ensure it's a perfect square. How can he prove that his garden is a square?

• All sides are congruent

• Diagonals are congruent

• All sides are congruent and diagonals are congruent

• All sides are parallel

Annabelle and Kayla are designing a new park and want to include a walking path in the shape of an Isosceles Trapezoid. How can they prove the path is an Isosceles Trapezoid?

• One pair of sides is parallel

• One pair of sides is parallel and the non parallel sides are congruent

• Opposite sides are congruent

• Show the figure has 4 sides

Nili and Eliana are designing a kite for a school project. They want to ensure that the kite is a perfect rhombus. How can they prove that their kite is a rhombus?

• All sides are congruent

• Diagonals are congruent

• All sides are congruent and diagonals are congruent

• All sides are parallel

Eliana and Ariella are building a triangular garden. How can they prove that their garden is an isosceles triangle?

• Prove all sides are different lengths

• Show that the three sides satisfy the Pythagorean theorem

• Show that opposite angles are congruent

• Show that two sides are congruent

To prove that quadrilateral JKLM is a parallelogram, given the coordinates of its vertices, Sara decided to show the diagonals bisect each other. To do so, which calculation must Sara perform?

• Find the lengths of the diagonals.

• Find the slope of each diagonal.

• Find the midpoint of each diagonal.

• Find the midpoint of each side.

• Find the slope of 2 sides.

• Find the slope of all 4 sides.

• Find the slope of the diagonals.

• Find the length of all 4 sides.