Parallelograms Rectangles Rhombi and Squares

6-4 Properties of Rhombuses, Rectangles, and Squares

Learning Objectives: 1) I can define and classify special types of parallelograms. 2) I can use properties of diagonals of rhombuses and rectangles.

Match

Match the following (IMPORTANT VOCABULARY):

• A parallelogram with four congruent sides

• A parallelogram with four right angles

• A parallelogram with four congruent sides AND four right angles.

Rhombus

Rectangle

Square

• Rhombus

• Rectangle

• Square

On the next slide, you will see the Quadrilateral Family Tree.. We will learn about ALL of the quadrilaterals mentioned, but today we will be focusing on rhombuses, rectangles, and squares.

Multiple Choice

A rectangle is always a parallelogram:

• True

• False

Multiple Choice

A parallelogram is always a rectangle:

• True

• False

Multiple Choice

The diagonals of a rectangle are

• parallel
• congruent
• perpendicular
• not congruent

Multiple Choice

If the figure is a rectangle, the value of x is...

• 2
• 12
• 13
• 28

Multiple Choice

HIJK is a rectangle. Find the value of length of each diagonal.
HJ = 3x + 5  and IK = 5x - 9 

• 7
• 14
• 26
• 7/3

Multiple Choice

Find the value of x.

• x = 50

• x = 40

• x = 30

• x = 90

Multiple Choice

A rhombus is a always parallelogram:

• True

• False

Multiple Choice

A parallelogram is a always rhombus:

• True

• False

​What are the measures of the numbered angles in rhombus ABCD?

∠1 = 90° (Diagonals are perp.)
∠2 = 58° (Diagonals bisect opp. angles which are congruent)
∠3 = 58° (Diagonals bisect opp. angles which are congruent)
∠4 = 32° (The angles of a Δ add up to 180°. Once you know ∠1 and ∠3, you can solve for ∠4.)

Finding Angle Measures

Multiple Choice

The diagonals of a rhombus 

• never intersect
• bisect the opposite angles
• are congruent
• bisect the sides

Multiple Choice

The diagonals of a rhombus are

• parallel
• congruent
• perpendicular
• equal to the side lengths

Multiple Choice

Find the values of x that makes the parallelogram a rhombus.

• 5

• 10

• 15

• 25

Multiple Choice

Find the value of x.

• x = 1

• x = 3

• x = 2

• x = 0

Multiple Choice

Find m∠2.

• 62
• 28
• 90
• 78

Multiple Choice

Find the measure of angle 1

• 54
• 108
• 72
• 36

Multiple Choice

A square is a rhombus.

• always true

• sometimes true

• never true

Multiple Choice

A square is a rectangle:

• always true

• sometimes true

• never true

Multiple Choice

A square has all the properties of a:

• parallelogram
• rectangle
• rhombus
• parallelogram, rectangle, and rhombus

Multiple Choice

MNKL is a square. Find the measure of angle MKN.

• 180 degrees

• 90 degrees

• 60 degrees

• 45 degrees