8.4 – Properties of Rhombuses, Rectangles And Squares

Both Opp. Sides parallel Parallelogram:   Both Opp. Sides parallel Both Opp. Sides  Both Opp. Angles  Consecutive Angles Supp. x + y = 180° y x y x Diagonals bisect each other

Parallelogram Rhombus Rectangle

Rhombus: Parallelogram with 4 congruent sides Diagonals are  Diagonals bisect opposite angles

Parallelogram Rhombus Rectangle

Rectangle: Parallelogram with 1 right angle Diagonals are congruent

Parallelogram Rhombus Rectangle Square

Square: A rectangle that is a rhombus

1. Determine the most specific name for the quadrilateral. Explain. Rhombus Diagonals are 

1. Determine the most specific name for the quadrilateral. Explain. Rectangle Quad w/ 4 right angles

1. Determine the most specific name for the quadrilateral. Explain. Rhombus 4 sides 

1. Determine the most specific name for the quadrilateral. Explain. Parallelogram Both pairs of opposite sides parallel

1. Determine the most specific name for the quadrilateral. Explain. Rectangle Diagonals are 

1. Determine the most specific name for the quadrilateral. Explain. Square Rectangle from diagonals being  Rhombus from diagonals being 

mQPR = 30° mQTP = 90° mPQT = 60° RP = 12 2. The diagonals of rhombus PQRS intersect at T. Given that mRPS = 30° and RT = 6, find the indicated measure. mQPR = 30° 60° 30° mQTP = 90° mPQT = 60° RP = 12

3. The diagonals of rectangle WXYZ intersect at P 3. The diagonals of rectangle WXYZ intersect at P. Given that mYXZ = 50° and XZ = 12, find the indicated measure. 40° WXZ = 40° PY = 6

4. The diagonals of square DEFG intersect at H 4. The diagonals of square DEFG intersect at H. Given that EH = 5, find the indicated measure. GHF = 90° DGH = 45° 45° HF = 5

all sides are congruent HW Problem Section Page # Assignment Spiral 8.4 537-538 19-26, 28, 32-35, 38-41, 44-48 9-13 #26 Ans: Rhombus all sides are congruent x + 104 = 180 3y = y + 8 x = 76° y = 4