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Properties of Quadrilaterals

Properties of Quadrilaterals. Lesson 5.5. Properties of parallelograms. Opposite sides are parallel and congruent Opposite angles are congruent Diagonals bisect each other Any pair of consecutive angles are supplementary. Properties of rectangles:. All properties of parallelograms apply

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Properties of Quadrilaterals

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  1. Properties of Quadrilaterals Lesson 5.5

  2. Properties of parallelograms • Opposite sides are parallel and congruent • Opposite angles are congruent • Diagonals bisect each other • Any pair of consecutive angles are supplementary

  3. Properties of rectangles: • All properties of parallelograms apply • All angles are right angles • Diagonals are congruent

  4. 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) x W y z

  5. 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.

  6. Properties of a square: • All properties of a rectangle • All properties of a rhombus • The diagonals form four isosceles triangles (45-45-90)

  7. 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

  8. 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. A Z V R The opposite sides of a parallelogram are congruent, so we can write two equations. 2x – 4 = ½ x + 8 3/2x – 4 = 8 3/2x = 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.

  9. Given: Rectangle MPRS MO congruent to PO Prove: ΔROS is isosceles S R P O M □ MPRS MO  PO SM  RP M is a rt  P is a rt  M  P ΔSMO  ΔRPO SO  RO ΔROS is isos. Given Given Opp sides  in a □. In a □, all s are rt s. Same as 4. All rts are  . SAS CPCTC An isosΔ has 2 sides  .

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