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) y W x 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. 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.

9. 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 .