1. 6-4 special parallelograms
Chapter 6
6-4 special parallelograms

2. Objectives
Prove and apply properties of rectangles, rhombuses, and squares.
Use properties of rectangles, rhombuses, and squares to solve problems.

3. Special parallelogram
A second type of special quadrilateral is a rectangle. A rectangle is a quadrilateral with four right angles.

4. Properties of rectangle

5. Properties of parallelogram
Since a rectangle is a parallelogram by Theorem 6-4-1, a rectangle “inherits” all the properties of parallelograms that you learned in Lesson 6-2.

6. Craft application
A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm. Find HM.
KM = JL = 86

7. Application Carpentry The rectangular gate has diagonal braces.
Find HJ.
HJ = GK = 48

8. Properties
A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides.

9. Properties
Like a rectangle, a rhombus is a parallelogram. So you can apply the properties of parallelograms to rhombuses.

10. Example 2A: Using Properties of Rhombuses to Find Measures
TVWX is a rhombus. Find TV.
WV = XT

11. Example
TVWX is a rhombus. Find mVTZ.

12. Example
CDFG is a rhombus. Find CD.

13. Squares
A square is a quadrilateral with four right angles and four congruent sides. In the exercises, you will show that a square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three.

14. Example 3: Verifying Properties of Squares
Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other.

15. Solution

16. Example 4: Using Properties of Special Parallelograms in Proofs
Given: ABCD is a rhombus. E is the midpoint of AB , and F is the midpoint of CD .
Prove: AEFD is a parallelogram.

17. Solution ||

18. Example
Given: PQTS is a rhombus with diagonal
Prove:

19. Solution Statements Reasons 1. PQTS is a rhombus. 3. QPR  SPR 2. 4.5. 6. 7.

20. Homework
Do problems 2-9 in your book page 424