8.4 – Properties of Rhombuses, Rectangles And Squares

8.4 – Properties of Rhombuses, RectanglesAnd Squares

Parallelogram:

Both Opp. Sides parallel

Both Opp. Sides

Both Opp. Angles

Consecutive Angles Supp.

Diagonals bisect each otherx

xyy

x + y = 180°

Parallelogram

Rhombus Rectangle

Rhombus:

• Parallelogram with 4 congruent sides

• Diagonals are

• Diagonals bisect opposite angles

Parallelogram

Rhombus Rectangle

Rectangle:

• Parallelogram with 4 right angles

• 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

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

1. Determine the most specific name for the quadrilateral. Explain.

2. The diagonals of rhombus PQRS intersect at T. Given that mRPS = 30° and RT = 6, find the indicated measure.

mQPR = 30°30°

mQTP = 90°

RP = 12

mPQT = 60°

60°

3. The diagonals of rectangle WXYZ intersect at P. Given that mYXZ = 50° and XZ = 12, find the indicated measure.

WXZ = 40°

40°

PY = 6

4. The diagonals of square DEFG intersect at H. Given that EH = 5, find the indicated measure.

GHF = 90°

DGH =45°

HF = 545°

Ans: Rhombus

all sides are congruent

x + 104 = 180

x = 76°

3y = y + 8

y = 4

HW Problem