Class Greeting

Special Quadrilaterals Chapter 6 - Lesson 4 Special Quadrilaterals

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

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

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

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

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

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

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

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

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

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

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

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.

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 .

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 .

Kahoot!

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

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

Stand Up Please