64 Notes.notebook
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October 02, 2012
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Prove and apply properties of rectangles, rhombuses, and squares.
Use properties of rectangles, rhombuses, and squares to solve problems.
Objectives
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A second type of special quadrilateral is a rectangle. A rectangle is a quadrilateral with four right angles.
Since a rectangle is a parallelogram by Theorem 641, a rectangle “inherits” all the properties of parallelograms that you learned in Lesson 62.
64 Notes.notebook
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October 02, 2012
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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.
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Check It Out! Example 1a Carpentry The rectangular gate has diagonal braces. Find HJ.
HJ = GK = 48
64 Notes.notebook
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October 02, 2012
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Check It Out! Example 1b
Carpentry The rectangular gate has diagonal braces. Find HK.
JL = LG
JG = 2JL = 2(30.8) = 61.6
Oct 14:05 PM
A rhombus is another special quadrilateral. A rhombus is a quadrilateral with four congruent sides.
Like a rectangle, a rhombus is a parallelogram. So you can apply the properties of parallelograms to rhombuses.
64 Notes.notebook
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October 02, 2012
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Example 2A: Using Properties of Rhombuses to Find Measures
TVWX is a rhombus. Find TV.
Def. of rhombus
Substitute given values.
Subtract 3b from both sides and add 9 to both sides.Divide both sides by 10.
WV = XT
13b – 9 = 3b + 4
10b = 13
b = 1.3
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Example 2B: Using Properties of Rhombuses to Find Measures
Subtract 20 from both a = 5
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October 02, 2012
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Check It Out! Example 2a
CDFG is a rhombus. Find CD.
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Check It Out! Example 2b
CDFG is a rhombus. Find the measure.
64 Notes.notebook
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October 02, 2012
Oct 21:27 PM
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A square is a quadrilateral with four right angles and four congruent sides. A square is a parallelogram, a rectangle, and a rhombus. So a square has the properties of all three.
64 Notes.notebook
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October 02, 2012
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Example 3: Verifying Properties of Squares
Show that the diagonals of square EFGH are congruent perpendicular bisectors of each other.
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Check It Out! Example 3
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Example 4: Using Properties of Special Parallelograms in Proofs
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Check It Out! Example 4
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64 Notes.notebook
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October 02, 2012
Oct 14:35 PM
Assignment(p. 407) 26 Hint: Use congruent opposite angles and transitive(p. 414) 1114, 1619, 21, 23, 26, 27(p. 424) 14, 15, 18, 20, 22, 35, 40, 41, 42, 48
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