Bell Ringer

Rhombus, Rectangles, and Squares

Rhombus- is a parallelogram with four congruent sides.

Rectangle – is a parallelogram with four right angles

Square – is a parallelogram with four congruent sides and four right angles

Use Properties of Special ParallelogramsExample 1

In the diagram, ABCD is a rectangle.

Find AD and AB.a.

By definition, a rectangle has four right angles, so mA = mB = mC = mD = 90°.

b.

SOLUTION

By definition, a rectangle is a parallelogram, so ABCD is a parallelogram. Because opposite sides of a parallelogram are congruent, AD = BC = 5 and AB = DC = 8.

a.

b. Find mA, mB, mC, and mD.

Now You Try Use Properties of Special Parallelograms

In the diagram, PQRS is a rhombus.Find QR, RS, and SP.

1.

ANSWER QR = 6, RS = 6, SP = 6

Identify Special QuadrilateralsExample 2

Use the information in the diagram to name the special quadrilateral.

SOLUTION

Because all of the sides are not the same length, you know that the quadrilateral is not a square.

The quadrilateral has four right angles. So, by the Rectangle Corollary, the quadrilateral is a rectangle.

Now You Try Identify Special Quadrilaterals

ANSWER rhombus

ANSWER square

Use the information in the diagram to name the special quadrilateral.

2.

3.

Use Diagonals of a RhombusExample 3

ABCD is a rhombus. Find the value of x.

By the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. So, x = 90 – 60 = 30.

SOLUTION

By Theorem 6.10, the diagonals of a rhombus are perpendicular. Therefore, BEC is a right angle, so ∆BEC is a right triangle.

Use Diagonals of a RectangleExample 4

b. The frame is not a rectangle because the diagonals are not congruent.

SOLUTION

The frame is a parallelogram because both pairs of opposite sides are congruent.

a.

The diagonals measure 7 ft 4 in. and7 ft 2 in. Is the frame a rectangle?

b.

You nail four pieces of wood together to build a four-sided frame, as shown. What is the shape of the frame?

a.

Now You Try Use Diagonals

ANSWER 90

ANSWER 12

ANSWER 45

Find the value of x.

rhombus ABCD4.

rectangle EFGH5.

square JKLM6.

Now You Try

Now You Try

Now You Try

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A B

CD

5xABCD is a square

find x

19.Now You Try

Page 328

Complete Pages 328-330#s 8-30 Even only