# Rhombi And Squares Chapter 6 Section 5. Rhombus A rhombus is a parallelogram with four congruent sides.

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Rhombi And Squares Chapter 6 Section 5

Rhombus A rhombus is a parallelogram with four congruent sides

Properties of a Rhombus Opposite 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 Square Opposite 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

Example We 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 AND FOUR 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 SIDES AND 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...

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