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Class Greeting
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Special Quadrilaterals
Chapter 6 - Lesson 4 Special Quadrilaterals
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Objective: The students will be able to apply properties of Rectangles.
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Vocabulary rectangle A second type of special quadrilateral is a rectangle. A rectangle is a quadrilateral with four right angles.
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Since a rectangle is a parallelogram
Since a rectangle is a parallelogram. You can apply the properties of parallelograms to rectangles.
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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
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Quadrilateral RSTU is a rectangle. If and find x.
Example 4-1a
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Quadrilateral EFGH is a rectangle. If and find x.
Answer: x = 5 Example 4-1c
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Quadrilateral LMNP is a rectangle. Find x.
Example 4-2a
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Quadrilateral LMNP is a rectangle. If x = 10, find y.
Example 4-2c
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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
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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
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When you are given a parallelogram with certain
properties, you can use the theorems below to determine whether the parallelogram is a rectangle.
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Example 1: Carpentry Application
A manufacture builds a mold for a desktop so that , , and mABC = 90°. Why must ABCD be a rectangle? Both pairs of opposites sides of ABCD are , so ABCD is a . Since mABC = 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.
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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 .
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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 .
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Kahoot!
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Lesson Summary: Objective: The students will be able to apply properties of Rectangles.
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Preview of the Next Lesson:
Objective: The students will be able to apply properties of Rhombi and Squares.
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Stand Up Please
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