1. Properties of Special Parallelograms
Geometry 6.4
Properties of Special Parallelograms

2. Learning Targets Students should be able to…
Prove and apply properties of rectangles, rhombuses, and squares.
Use properties of rectangles, rhombuses, and squares to solve problems.

3. Warm-up

4. 6.1 – 6.3
Clear desks.
It is now time to take the quiz.

5. Vocabulary Term Name Diagram Additional Notes Rectangle Rectangle ABCD
a quadrilateral with four right angles. B C A D

6. Vocabulary Term Name Diagram Additional Notes Rectangle Rectangle ABCD
a quadrilateral with four right angles.
Rhombus
Rhombus ABCD
A quadrilateral with four congruent sides B C A D B C A D

7. Vocabulary Term Name Diagram Additional Notes Rectangle Rectangle ABCD
a parallelogram with four right angles.
Rhombus
Rhombus ABCD
A parallelogram with four congruent sides
Square
Square ABCD
- A parallelogram` with four right angles and four congruent sides B C A D B C A D B C A D

8. Venn Diagram Rectangle Rhombus
Here is a Venn Diagram for the information today. We will be adding to this and recording it in our Quadrilateral Summary Sheet. P A R L E O G M S q u a r e
Rectangle
Rhombus

9. Always, Sometimes, or Never
a. A rhombus is a rectangle.
b. A parallelogram is a rectangle.
c. A square is a rhombus
d. A rhombus is a parallelogram

10. Properties of Rectangles

11. Properties of Rhombuses

12. Properties of Squares Parallelogram Rectangle Rhombus Square
A square has the features of both rhombuses and rectangles!!
Parallelogram
Rectangle
Rhombus
Square

13. Example If ABCD is a rectangle, what do you know about ABCD?
4 right angles (by definition of rectangle)
Opposite sides are congruent and parallel (definition of parallelogram)
Opposite angles are congruent (since parallelogram)
Consecutive angles are supplementary (since parallelogram)
Diagonals bisect each other. (since parallelogram)

14. Corollaries about Special Quadrilaterals
Rhombus:
A quadrilateral is a rhombus if and only if it has four congruent sides.
Rectangle:
A quadrilateral is a rectangle if and only if it has four right angles.
Square:
A quadrilateral is a square if and only if it is a rhombus and a rectangle.

15. Time To Use The Theorems
Ex: PQRS is a rhombus.
If PS = 2y + 3 and SR = 5y – 6, what is the value of y?

16. Time To Use The Theorems
Example: RSTV is a rhombus. Find VT

17. Time To Use The Theorems
Example: RSTV is a rhombus. Find 𝑚∠𝑊𝑆𝑅.
(y+2)
(2y+10)

18. Your Turn! Try on your own!
Ex: In rectangle ABCD, if AB = 7x – 3 and CD = 4x + 9, then find the value of x.
(a) (b) (c) (d) (e) 5

19. Verifying Properties of Squares
You must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

20. Verifying Properties of Squares
You must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

21. Verifying Properties of Squares
You must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

22. Verifying Properties of Squares
You must show that the diagonals of square ABCD are congruent perpendicular bisectors of each other. A(-1, 0), B(-3, 5), C(2, 7), D(4, 2).

23. Verifying Properties of Squares
Another Try! If needed on one sheet of paper.

24. Practice B

25. Practice B

26. Practice B

27. Extra Practice

28. Extra Practice

29. Extra Practice