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