7.4 Properties of Special Parallelograms

OBJ: Students will be able to use properties of special parallelograms and diagonals of special parallelograms.

Do Now

RhombusA parallelogram with four congruent

sides.

RectangleA parallelogram with four right angles.

SquareA parallelogram with four

congruent sides and four right angles.

Rhombus CorollaryA 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.

1. For any rectangle ABCD, decide whether the statement is always or sometimes true. Explain your reasoning.

a. AB = BC

b. AB = CB

2. For any square JKLM, is it always or sometimes true that . Explain your reasoning.

Do NowWhat classifies a parallelogram as a rhombus, rectangle and square? i.e. what characteristics do each have.

Rhombus Diagonals TheoremA parallelogram is a rhombus if and

only if its diagonals are perpendicular.

Rhombus Opposite Angles TheoremA parallelogram is a rhombus if

and only if each diagonal bisects a pair of opposite angles.

3. Find the measures of the numbered angles in rhombus ABCD.

4. Find the measures of the numbered angles in rhombus DEFG.

Rectangle Diagonals TheoremA parallelogram is a rectangle if

and only if its diagonals are congruent.

5. In rectangle QRST, QS= 5x – 31 and RT = 2x + 11. Find the lengths of the diagonals of QRST.

HWPg. 393 #3,5, 13-16, 25-33 odds