GH­­Lesson 6­5_notes.notebook November 18, 2015

6.5 Rhombi and Squares

Students will be able to . . .

• recognize and apply the properties of rhombi and squares.

• determine whether quadrilaterals are rectangles, rhombi or squares.

GH­­Lesson 6­5_notes.notebook November 18, 2015

Rhombus

*Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Consecutive angles are supplementary

Diagonals bisect each other

Unique properties of a rhombus

All four sides are congruent.

Diagonals are perpendicular.

Diagonals bisect opposite angles.

GH­­Lesson 6­5_notes.notebook November 18, 2015

Square

Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Consecutive angles are supplementary

Diagonals bisect each other

Rectangle

Four right angles

Diagonals are congruent

Rhombus

All sides are congruent

Diagonals are perpendicular

Diagonals bisect opposite angles

GH­­Lesson 6­5_notes.notebook November 18, 2015

How to determine a parallelogram is a rectangle, rhombus, square or parallelogram.

1. Find the slopes of the diagonals. Make note of whether or not the diagonals are perpendicular.

2. Find the lengths of the diagonals. Make note of whether or not the diagonals are congruent.

3. Interpret the results of steps 1 & 2.

(a) Diagonals are perpendicular, but are not congruent ­­ rhombus

(b) Diagonals are not perpendicular, but are congruent ­­ rectangle

(c) Diagonals are perpendicular and congruent ­­ square

(d) Diagonals are not perpendicular and are not congruent ­­ parallelogram

GH­­Lesson 6­5_notes.notebook November 18, 2015

GH­­Lesson 6­5_notes.notebook November 18, 2015

GH­­Lesson 6­5_notes.notebook November 18, 2015

J

K

L

M

Find the perimeter of rhombus JKLM, if JL = 16 and KM = 12.

Use rhombus XYZW with m WYZ = 49, VW = 3, XV = 2a ­ 2 and ZV = . 5a + 1

4

X Y

W Z

VFind

(a) m YZV

(b) m XYW

(c) XZ

(d) XW

What is the perimeter of rhombus XYZW?