Bell Ringer

1 / 11

# Bell Ringer - PowerPoint PPT Presentation

Bell Ringer. Rhombi Rectangles &amp; Squares. Rhombus. Definition:. A rhombus is a parallelogram with four congruent sides. Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. ≡. ≡.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Bell Ringer' - jerry-cook

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Bell Ringer

Lesson 6-4: Rhombus & Square

Rhombi

Rectangles &

Squares

Rhombus

Definition:

A rhombus is a parallelogram with four congruent sides.

• Opposite sides are parallel.
• Opposite sides are congruent.
• Opposite angles are congruent.
• Consecutive angles are supplementary.
• Diagonals bisect each other

Since a rhombus is a parallelogram the following are true:

Properties of a Rhombus

Theorem:

The diagonals of a rhombus are perpendicular.

Theorem:

Each diagonal of a rhombus bisects a pair of opposite angles.

Rhombus Examples .....

Given: ABCD is a rhombus. Complete the following.

• If AB = 9, then AD = ______.
• If m<1 = 65, the m<2 = _____.
• m<3 = ______.
• If m<ADC = 80, the m<DAB = ______.
• If m<1 = 3x -7 and m<2 = 2x +3, then x = _____.

9 units

65°

90°

100°

10

Square

Definition:

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

• Opposite sides are parallel.
• Four right angles.
• Four congruent sides.
• Consecutive angles are supplementary.
• Diagonals are congruent.
• Diagonals bisect each other.
• Diagonals are perpendicular.
• Each diagonal bisects a pair of opposite angles.

Since every square is a parallelogram as well as a rhombus and rectangle, it has all the properties of these quadrilaterals.

Squares – Examples…...

Given: ABCD is a square. Complete the following.

• If AB = 10, then AD = _____ and DC = _____.
• If CE = 5, then DE = _____.
• m<ABC = _____.
• m<ACD = _____.
• m<AED = _____.

10 units

10 units

5 units

90°

45°

90°

Rectangles

Definition:

A rectangle is a parallelogram with four right angles.

• Opposite sides are parallel.
• Opposite sides are congruent.
• Opposite angles are congruent.
• Consecutive angles are supplementary.
• Diagonals bisect each other.

A rectangle is a special type of parallelogram.

Thus a rectangle has all the properties of a parallelogram.

A

B

E

D

C

Properties of Rectangles

Theorem:

If a parallelogram is a rectangle, then its diagonals are congruent.

Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles.

Converse:

If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle.

A

B

2

3

1

E

4

5

6

D

C

Examples…….
• If AE = 3x +2 and BE = 29, find the value of x.
• If AC = 21, then BE = _______.
• If m<1 = 4x and m<4 = 2x, find the value of x.
• If m<2 = 40, find m<1, m<3, m<4, m<5 and m<6.

x = 9 units

10.5 units

x = 18 units

m<1=50,

m<3=40,

m<4=80,

m<5=100,

m<6=40