7.4 Properties of Special Parallelograms OBJ: Students will be able to use properties of special parallelograms and diagonals of special parallelograms.

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7.4 Properties of Special Parallelograms OBJ: Students will be able to use properties of special parallelograms and diagonals of special parallelograms.

Do Now

Rhombus A parallelogram with four congruent sides.

Rectangle A parallelogram with four right angles.

Square A parallelogram with four congruent sides and four right angles.

Rhombus Corollary A quadrilateral is a rhombus if and only if it has four congruent sides.

Rectangle Corollary A quadrilateral is a rectangle if and only if it has four right angles.

Square Corollary A 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 Now What classifies a parallelogram as a rhombus, rectangle and square? i.e. what characteristics do each have.

Rhombus Diagonals Theorem A parallelogram is a rhombus if and only if its diagonals are perpendicular.

Rhombus Opposite Angles Theorem A 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 Theorem A parallelogram is a rectangle if and only if its diagonals are congruent.

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

HW Pg. 393 #3,5, 13-16, odds