1. Class Greeting

2. Special Quadrilaterals
Chapter 6 - Lesson 4
Special Quadrilaterals

3. Objective: The students will be able to apply properties of Rectangles.

4. Vocabulary
rectangle
A second type of special quadrilateral is a rectangle. A rectangle is a quadrilateral with four right angles.

5. Since a rectangle is a parallelogram
Since a rectangle is a parallelogram. You can apply the properties of parallelograms to rectangles.

6. Example 1: Craft Application
A woodworker constructs a rectangular picture frame so that JK = 50 cm and JL = 86 cm.
Find HM.
JL  KM
The diagonals of a rectangle are congruent
JL = KM
Definition of congruent segments
KM = 86
Substitution
KM = KH + HM
Segment Addition Postulate
KH = HM
The diagonals of a rectangle bisect each other
86 = HM + HM
Substitution
86 = 2HM
Simplify
43 = HM
Division
Symmetric Property
HM = 43

7. Quadrilateral RSTU is a rectangle. If and find x.
Example 4-1a

8. Quadrilateral EFGH is a rectangle. If and find x.
Answer: x = 5
Example 4-1c

9. Quadrilateral LMNP is a rectangle. Find x.
Example 4-2a

10. Quadrilateral LMNP is a rectangle. If x = 10, find y.
Example 4-2c

11. Quadrilateral ABCD has vertices A(–2, 1), B(4, 3), C(5, 0), and D(–1, –2). Determine whether ABCD is a rectangle using the Slope Formula.
Answer: The sides create four right angles. Therefore, ABCD is a rectangle.
Example 4-4a

12. The sides create four right angles. Therefore, ABCD is a rectangle.
Quadrilateral WXYZ has vertices W(–2, 1), X(–1, 3), Y(3, 1), and Z(2, –1). Determine whether WXYZ is a rectangle using the Slope Formula.
Answer:
the slope of WX is 2;
the slope of YZ is 2;
the slope of XY is -1/2;
the slope of WZ is -1/2.
The sides create four right angles. Therefore, ABCD is a rectangle.
Example 4-4f

13. When you are given a parallelogram with certain
properties, you can use the theorems below to determine whether the parallelogram is a rectangle.

14. Example 1: Carpentry Application
A manufacture builds a mold for a desktop so that , , and mABC = 90°. Why must ABCD be a rectangle?
Both pairs of opposites sides of ABCD are ,
so ABCD is a .
Since mABC = 90°, one angle of ABCD is a right angle.
So ABCD is a rectangle because if one angle of a is a right angle then the is a rectangle.

15. Determine if the conclusion is valid
Determine if the conclusion is valid. If not, tell what additional information is needed to make it valid.
Given: ABC is a right angle.
Conclusion: ABCD is a rectangle.
The conclusion is not valid.
If one angle of a parallelogram is a right angle, then the parallelogram is a rectangle.
To apply this theorem, you need to know that ABCD is a .

16. Determine if the conclusion is valid
Determine if the conclusion is valid. If not, tell what additional information is needed to make it valid.
Given: AC = BD.
Conclusion: ABCD is a rectangle.
The conclusion is not valid.
The diagonals are congruent by definition of congruence and If diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
To apply this theorem, you need to know that ABCD is a .

17. Kahoot!

18. Lesson Summary:
Objective: The students will be able to apply properties of Rectangles.

19. Preview of the Next Lesson:
Objective: The students will be able to apply properties of Rhombi and Squares.

20. Stand Up Please