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Published byRosemary Edwards Modified over 9 years ago
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Properties of Quadrilaterals Lesson 5.5
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Properties of parallelograms Opposite sides are parallel and congruent Opposite angles are congruent Diagonals bisect each other Any pair of consecutive angles are supplementary
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Properties of rectangles: All properties of parallelograms apply All angles are right angles Diagonals are congruent
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Properties of a kite: Two disjoint pairs of consecutive sides are congruent Diagonals are perpendicular One diagonal is the perpendicular bisector of the other One diagonal bisects a pair of opposite angles (wy bisects <xwz and <xyz) One pair of opposite angles are congruent (<wxy and <wzy) y W x z
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Properties of a rhombus: All properties of parallelograms apply All properties of a kite apply All sides are congruent (equilateral) Diagonals bisect the angles Diagonals are perpendicular bisectors of each other Diagonals divide it into four congruent right triangles.
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Properties of a square: All properties of a rectangle All properties of a rhombus The diagonals form four isosceles triangles (45-45-90)
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Properties of an isosceles trapezoid: Legs are congruent (definition) Bases are parallel (definition) Lower base angles are congruent Upper base angles are congruent Diagonals are congruent Lower base angle is supplementary to upper base angle
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Given: ZRVA is a parallelogram AV = 2x – 4 RZ = ½ x + 8 VR = 3y + 5 ZA = y + 12 Find x. Find y. Find the perimeter. RV AZ The opposite sides of a parallelogram are congruent, so we can write two equations. 2x – 4 = ½ x + 8 3 / 2 x – 4 = 8 3 / 2 x = 12 x = 8 AV = 12 & RZ = 12 3y + 5 = y + 12 2y + 5 = 12 2y = 7 y = 3.5 VR = 15.5 & ZA = 15.5 The perimeter is 12 + 12 + 15.5 + 15.5 = 55 units.
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R P S M O Given: Rectangle MPRS MO congruent to PO Prove:ΔROS is isosceles 1. □ MPRS 2.MO PO 3.SM RP 4. M is a rt 5. P is a rt 6. M P 7.ΔSMO ΔRPO 8.SO RO 9.ΔROS is isos. 1.Given 2.Given 3.Opp sides in a □. 4.In a □, all s are rt s. 5.Same as 4. 6.All rt s are . 7.SAS 8.CPCTC 9.An isos Δ has 2 sides .
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