Rhombi And SquaresChapter 6 Section 5

Rhombus

A rhombus is a parallelogram with four congruent sides

Properties of a RhombusOpposite sides are congruent

Opposite angles are congruent

Consecutive angles are supplementary

Diagonals bisect each other

Plus, Diagonals are Perpendicular

And, Diagonals bisect each pair of opposite angles

Square

A square is a parallelogram with four congruent sides and four right angles.

Since a square is a parallelogram with four congruent sides, a square is also a Rhombus

Since a square is a parallelogram with four right angles, a square is also a rectangle.

Properties of a SquareOpposite sides are congruent (duh)

Opposite angles are congruent (duh)

Consecutive angles are supplementary

Diagonals bisect each other

Plus, diagonals are congruent (since a square is a rectangle)

Plus, diagonals are perpendicular (since a square is a rhombus)

And, diagonals bisect each pair of opposite angles (rhombus)

Diagonals of a Rhombus

ExampleWe know that the diagonals of a rhombus bisects the two angles of the rhombus and that the diagonals are perpendicular, so find the measures of the numbered angles in each of the following:

Something to think about....

SO, A SQUARE HAS ALL THE PROPERTIES OF A RECTANGLE AND A RHOMBUS

IN ORDER TO BE A RECTANGLE, THE ONLY STIPULATION IS A

PARALLELOGRAM WITH 4 RIGHT ANGLES.

DO YOU THINK A SQUARE IS ALWAYS A RECTANGLE?

IS A RECTANGLE ALWAYS A SQUARE?

IN ORDER TO BE A SQUARE IT MUST HAVE FOUR RIGHT ANGLES ANDFOUR CONGRUENT SIDES!!

IN ORDER TO BE A RHOMBUS, THE ONLY STIPULATION IS A PARALLELOGRAM

WITH FOUR CONGRUENT SIDES.

DO YOU THINK A SQUARE IS ALWAYS A RHOMBUS?

IN ORDER TO BE A SQUARE, THE FIGURE MUST HAVE 4 CONGRUENT SIDESAND FOUR RIGHT ANGLES!

IS A RHOMBUS ALWAYS A SQUARE?

What’s the most precise name? (parallelogram, rhombus, square, rectangle)

Find the value of the variables...

Try this one…(from your worksheet…)

Cute!

Have a great day!!!

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