1. Properties of Quadrilaterals

2. Standards
GEOMETRY 7.0 “Students prove and use theorems involving … the properties of quadrilaterals....”

3. Objectives Identify the properties of special quadrilaterals
Compare the properties of different quadrilaterals
Classify quadrilaterals by specific properties

4. What is a quadrilateral?
A quadrilateral is any polygon with 4 sides.

5. Types of Quadrilaterals!
We will study 7 types of special quadrilaterals.
Parallelogram
Rectangle
Rhombus
Square
Trapezoid
Isosceles Trapezoid
Kite

6. Parallelograms!

7. Properties of Parallelograms!
Both pairs of opposite sides are parallel.
Both pairs of opposite sides are congruent.

8. Properties of Parallelograms!
Both pairs of opposite angles are congruent.
Consecutive Angles are Supplementary.

9. Properties of Parallelograms!
The diagonals bisect each other, which means that …
… the two halves of each diagonal are congruent!

10. Rectangles!

11. Properties of Rectangles!
A rectangle is a special type of parallelogram, so all the properties of parallelograms also apply to rectangles…
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
The diagonals bisect each other

12. Properties of Rectangles!
All four angles are congruent. This means that …
… all four angles are right angles!

13. Properties of Rectangles!
The diagonals are congruent.

14. Rhombi!

15. Properties of Rhombi!
A rhombus is a special type of parallelogram, so all the properties of parallelograms also apply to rhombi…
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
The diagonals bisect each other

16. Properties of Rhombi!
All four sides are congruent!

17. Properties of Rhombi!
The diagonals bisect the interior angles.

18. Properties of Rhombi!
The diagonals are perpendicular.

19. Squares!

20. Properties of Squares!
A square is a special type of rectangle AND a special type of rhombus. Therefore, all the properties of rectangles and rhombi apply to squares.
Most importantly, a square has four congruent angles (like a rectangle) and four congruent sides (like a rhombus).

21. Trapezoids!

22. Properties of Trapezoids!
One pair of opposite sides are parallel. These sides are called the bases of the trapezoid.
The non-parallel sides are called legs.
Base 1
Leg
Leg
Base 2

23. Isosceles Trapezoids!

24. Properties of Isosceles Trapezoids!
An isosceles trapezoid is a special type of trapezoid.
One pair of opposite sides are parallel.
The non-parallel sides are congruent.

25. Properties of Isosceles Trapezoids!
The base angles are congruent.
Only angles on the same base are congruent!

26. Properties of Isosceles Trapezoids!
The diagonals are congruent.

27. Kites!

28. Properties of Kites!
Two pairs of adjacent sides are congruent.

29. Properties of Kites!
The diagonals are perpendicular, which means that …
…the diagonals meet at right angles!

30. Classify!
Create a tree map classifying the different types of quadrilaterals.
Remember, some quadrilaterals are special types of other quadrilaterals. If so, the special quadrilateral belongs under the other quadrilateral on the tree map.
Include as many representations of the information as possible, including sentences, pictures, examples, etc.