1. Quadrilaterals and Coordinates Proof
Review Topic IV
Opening routine

2. Topic IV: Quadrilaterals and Coordinate Proof

3. Quadrilaterals and Coordinates Proof
Review Topic IV
Objective: Use properties of parallelograms, rectangles, rhombi and squares to solve problems.
Essential Question: How the slope criteria for parallel lines can be used to determine if a quadrilateral is a parallelogram?

4. Quadrilaterals and Coordinates Proof
Review Topic IV
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
Review Topic IV
Vocabulary
Kite: Is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
Trapezoid: Is a quadrilateral with exactly one pair of parallel sides.
Base of a trapezoid: The parallel sides of a trapezoid are called bases.
Leg of a trapezoid: The non-parallel sides of trapezoid are called legs.

6. Quadrilaterals and Coordinates Proof
Review Topic IV
Vocabulary
Base angle of a trapezoid: The base angles are formed by a base and one of the legs.
Isosceles trapezoid: Is a special type of trapezoid in which non-parallel sides and base angles are equal.
Midsegment of a trapezoid: Is the segment whose endpoints are the midpoints of the legs. The midsegment is parallel to each base.

7. Quadrilaterals and Coordinates Proof
Review Topic IV

8. Quadrilaterals and Coordinates Proof
Review Topic IV

9. Quadrilaterals and Coordinates Proof
Review Topic IV

10. Quadrilaterals and Coordinates Proof
Review Topic IV

11. Quadrilaterals and Coordinates Proof
Review Topic IV

12. Quadrilaterals and Coordinates Proof
Review Topic IV

13. Quadrilaterals and Coordinates Proof
Review Topic IV

14. Quadrilaterals and Coordinates Proof
Review Topic IV
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.

15. Quadrilaterals and Coordinates Proof
Review Topic IV

16. Quadrilaterals and Coordinates Proof
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17. Quadrilaterals and Coordinates Proof
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18. Quadrilaterals and Coordinates Proof
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19. Quadrilaterals and Coordinates Proof
Review Topic IV

20. Quadrilaterals and Coordinates Proof
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21. Quadrilaterals and Coordinates Proof
Review Topic IV

22. Quadrilaterals and Coordinates Proof
Review Topic IV
Test for Rectangle in the Coordinate Plane
To prove if a quadrilateral in the coordinate plane is a rectangle, first proof the quadrilateral is a parallelogram, then it can be used two different methods:
Method 1: Show that the diagonals are congruent.
Method 2: Show that it has a right angle by using slope.

23. Quadrilaterals and Coordinates Proof
Review Topic IV

24. Quadrilaterals and Coordinates Proof
Review Topic IV
Test for Rhombus in the Coordinate Plane
To prove if a quadrilateral in the coordinate plane is a rhombus, first proof the quadrilateral is a parallelogram, then it can be used two different methods:
Method 1: Prove that the diagonals are perpendicular.
Method 2: Prove that a pair of adjacent sides are equal.
Method 3: Prove that all four sides are equal.

25. Quadrilaterals and Coordinates Proof
Review Topic IV
Conditions for squares
The conditions for squares are a combination of the conditions for rectangles and rhombi.
1. If one angle is a right angle
2. If the diagonals are congruent
3. If one pair of consecutive sides The
are congruent parallelogram
4. If the diagonals are perpendicular is a square
5. If one diagonal bisect a pair of
opposite angles

26. Quadrilaterals and Coordinates Proof
Review Topic IV
Test for Squares in the Coordinate Plane
To prove if a quadrilateral in the coordinate plane is a square, there are many ways to do this :
I recommend proving that:
1. Diagonals bisect each other (parallelogram).
2. Diagonals are congruent (only rectangles and squares).
3. Diagonals are perpendicular (only squares).

27. Quadrilaterals and Coordinates Proof
Review Topic IV

28. Quadrilaterals and Coordinates Proof
Review Topic IV

29. Quadrilaterals and Coordinates Proof
Review Topic IV

30. Quadrilaterals and Coordinates Proof
Review Topic IV

31. Quadrilaterals and Coordinates Proof
Review Topic IV .

32. Quadrilaterals and Coordinates Proof
Review Topic IV
Independent Practice - YOU DO
Worksheet “Review Topic IV”
Questions 16 – 25

33. Quadrilaterals and Coordinates Proof
Review Topic IV
Closure
Essential Question: How the slope criteria for parallel lines can be used to determine if a quadrilateral is a parallelogram?