Rhombi & SquaresSECTION 8.5

What are the properties of a rhombus, and how do I apply them?

What are the properties of squares, and how do I apply them?

Rhombi is plural of rhombus

RHOMBI AND SQUARES

Rhombus: A quadrilateral with all four sides congruent.

How does this compare to a parallelogram?

RHOMBUS

All properties of a parallelogram apply, so…

1. Opposite Sides are and 2. Opposite s are 3. Consecutive s are supplementary4. Diagonals bisect each other

New

5. Diagonals are perpendicular to each other6. Diagonals bisect opposite angles

PROPERTIES

Square – A quadrilateral that is a rhombus and rectangle.

SQUARE

All properties of a parallelogram and rectangle apply, so…

1. All Sides are 2. All s are (90°)3. Diagonals are 4. Diagonals bisect each other5. Diagonals are perpendicular to each other6. Diagonals bisect opposite angles

PROPERTIES OF A SQUARE

Use rhombus LMNP to find the value of y if m

EXAMPLE

N

In rhombus LMNP, MN = 2x + 3 and NP = 5x. Find x and MN.

EXAMPLE

N

Use rhombus LMNP to find m

EXAMPLE

N

Use rhombus ABCD and the given information to find the value of each variable.

Find

Find

EXAMPLE

E

Determine whether parallelogram EFGH is a rhombus, a rectangle or a square for E(0,-2), F(-3, 0), G(-1, 3) and H(2, 1). List all that apply. Explain.

EXAMPLE

Page 434 12 – 19 20 – 30 (Even) Skip 24!

Hint on #12 – a quadrilateral has 360°, so add up the four angles

HOMEWORK