1. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombus and squares
Opening routine
Find x and y if the quadrilateral is a parallelogram

2. Topic IV: Quadrilaterals and Coordinate Proof

3. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares
Objective: Use congruency between triangles to prove that a quadrilateral is rectangle.
Essential Question: What properties can be used to determine if a quadrilateral is a rectangle?

4. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares
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.

5. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares
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.

6. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

7. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

8. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

9. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

10. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

11. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

12. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares
Use the properties of the rectangles to find the measures of 1 and 2.
As the triangles form by the diagonal MP are right triangles, then:
(3x)o + (2x + 20)o + 90o = 180o
3x + 2x + 20 = 90o
5x = 70o
x = 14o
As 1 and QMP are complementary,
1 + QMP = 90o
1 + 3x = 90o
1 + 3(14) = 90o
1 + 42o = 90o
1 = 48o
As 2 and QMP are alternate interior angles, then 2 = 42o.

13. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

14. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

15. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

16. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

17. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

18. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

19. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares

20. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares
Guided Practice – WE DO
Points ABCD are midpoints
of the sides of the larger
square. If the larger square
has area 60, what's the small
square's area?
A) 20 B) 25 C) 30 D) 45

21. Quadrilaterals and Coordinates Proof
Properties of rectangles, rhombi and squares
Independent Practice - YOU DO
Worksheet “Properties of rectangles, rhombi and squares”
Exercises from 1 to 24

22. 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?