2 Review Find the value of the variables. p + 50° + (2p – 14)° = 180° 52°(2p-14)°50°68°p + 50° + (2p – 14)° = 180°p + 2p + 50° - 14° = 180°3p ° = 180°3p = 144 °p = 48 °52° + 68° + h = 180°120° + h = 180 °h = 60°
3 Special Parallelograms RhombusA rhombus is a parallelogram with four congruent sides.
4 Special Parallelograms RectangleA rectangle is a parallelogram with four right angles.
5 Special Parallelogram SquareA square is a parallelogram with four congruent sides and four right angles.
6 Corollaries Rhombus corollary Rectangle corollary Square corollary A quadrilateral is a rhombus if and only if it has four congruent sides.Rectangle corollaryA quadrilateral is a rectangle if and only if it has four right angles.Square corollaryA quadrilateral is a square if and only if it is a rhombus and a rectangle.
7 Example PQRS is a rhombus. What is the value of b? 2b + 3 = 5b – 6
8 Review In rectangle ABCD, if AB = 7f – 3 and CD = 4f + 9, then f = ___ 123457f – 3 = 4f + 93f – 3 = 93f = 12f = 4
9 Example PQRS is a rhombus. What is the value of b? 3b + 12 = 5b – 6
10 Theorems for rhombusA parallelogram is a rhombus if and only if its diagonals are perpendicular.A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.L
11 Theorem of rectangleA parallelogram is a rectangle if and only if its diagonals are congruent.ABDC
12 Match the properties of a quadrilateral The diagonals are congruentBoth pairs of opposite sides are congruentBoth pairs of opposite sides are parallelAll angles are congruentAll sides are congruentDiagonals bisect the anglesParallelogramRectangleRhombusSquareB,DA,B,C,DA,B,C,DB,DC,DC
13 Decide if the statement is sometimes, always, or never true. A rhombus is equilateral.2. The diagonals of a rectangle are _|_.3. The opposite angles of a rhombus are supplementary.4. A square is a rectangle.5. The diagonals of a rectangle bisect each other.6. The consecutive angles of a square are supplementary.AlwaysSometimesSometimesAlwaysAlwaysAlwaysQuadrilateral ABCD is Rhombus.7. If m <BAE = 32o, find m<ECD.8. If m<EDC = 43o, find m<CBA.9. If m<EAB = 57o, find m<ADC.10. If m<BEC = (3x -15)o, solve for x.11. If m<ADE = ((5x – 8)o and m<CBE = (3x +24)o, solve for x12. If m<BAD = (4x + 14)o and m<ABC = (2x + 10)o, solve for x.A BED C32o86o66o35o1626
14 Coordinate Proofs Using the Properties of Rhombuses, Rectangles and Squares Using the distance formula and slope, how can we determine the specific shape of a parallelogram?Rhombus –Rectangle –Square -1. Show all sides are equal distance2. Show all diagonals are perpendicular.1. Show diagonals are equal distance2. Show opposite sides are perpendicularShow one of the above four ways.Based on the following Coordinate values, determine if each parallelogramis a rhombus, a rectangle, or square.P (-2, 3) P(-4, 0)Q(-2, -4) Q(3, 7)R(2, -4) R(6, 4)S(2, 3) S(-1, -3)RECTANGLERECTANGLE