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angle A shape formed by two rays that share an endpoint

closed shape A shape that begins and ends at the same point

polygon A closed plane shape made up of straight line segments

quadrilateral A polygon with four sides and four angles

Dear Family,During the next few weeks, our math class will be learning about plane shapes. We will learn to identify polygons and describe them by their sides and angles.You can expect to see homework that provides practice with shapes.Here is a sample of how your child will be taught to classify quadrilaterals.

12

Classify Quadrilaterals

Use sides and angles to name this quadrilateral.

STEP 1 There are 2 right angles.

STEP 2 There is exactly 1 pair of opposite sides that are parallel.

So, the quadrilateral is a trapezoid.

ActivityPoint out everyday objects that resemble plane shapes, such as books, photos, windows, and traffic signs. Have your child identify the shape and describe it by its sides and angles.

Chapter 12 P237

Checking Angles

The corner of a sheet of paper or an index card can be used to check whether an angle in a polygon is right, less than a right angle, or greater than a right angle.

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Comprobar ángulos

Puedes usar la esquina de una hoja o de una tarjeta para comprobar si un ángulo de un polígono es recto, menor que un ángulo recto o mayor que un ángulo recto.

12

P238

ActividadSeñalen objetos cotidianos que parezcan figuras planas, como libros, fotografías, ventanas y señales de tráfico. Pida a su hijo o hija que identifique la figura y que la describa según sus lados y ángulos.

Clasificar cuadriláteros

ángulo Una figura compuesta por dos rayos que comparten un extremo

figura cerrada Una figura que comienza y termina en el mismo punto

polígono Una figura plana cerrada compuesta por segmentos rectos

cuadrilátero Un polígono con cuatro lados y cuatro ángulos

Querida familia,

Durante las próximas semanas, en la clase de matemáticas aprenderemos sobre figuras planas. Aprenderemos a identificar polígonos y a describirlos según sus lados y ángulos.

Llevaré a casa tareas para practicar con figuras.

Este es un ejemplo de cómo clasificaremos cuadriláteros.

Usa los lados y los ángulos para nombrar este cuadrilátero.

PASO 1 Hay dos ángulos rectos.

PASO 2 Hay exactamente 1 par de lados opuestos que son paralelos.

Por tanto, el cuadrilátero es un trapecio.

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Lesson 12.4

Describe Sides of Polygons

Look at the dashed sides of the polygon. Tell if they appear to be intersecting, perpendicular, or parallel. Write all the words that describe the sides.

Use shapes A–D for 10–11. 10. Which shapes appear to have parallel sides?

____

11. Which shapes appear to have perpendicular sides?

____

Chapter 12 P245

1.

____

2.

____

3.

____

4.

____

5.

____

6.

____

7.

____

8.

____

9.

____

COMMON CORE STANDARD MACC.3.G.1.1

Reason with shapes and their attributes.

parallel

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P246

Lesson Check (MACC.3.G.1.1)

1. How many pairs of parallel sides does the quadrilateral appear to have?

A 1 C 3

B 2 D 4

2. Which sides appear to be parallel?

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A a and c only

B b and d only

C a and b, c and d

D a and c, b and d

Spiral Review (MACC.3.NF.1.1, MACC.3.G.1.1)

3. Mr. Lance designed a class banner shaped like the polygon shown. What is the name of the polygon? (Lesson 12.3)

A pentagon C hexagon

B octagon D decagon

4. How many angles greater than a right angle does this shape have? (Lesson 12.2)

A 0 C 2

B 1 D 3

5. How many line segments does this shape have? (Lesson 12.1)

A 6 C 8

B 7 D 9

6. Which fraction names the shaded part? (Lesson 8.3)

A 1 __ 3 C 1 __ 6

B 1 __ 4 D 5 __ 6

MATHEMATICAL PRACTICESMATHEMATICAL PRACTICES

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Some quadrilaterals cannot be classified as a trapezoid, rectangle, square, or rhombus.

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Classify QuadrilateralsEssential Question How can you use sides and angles to help you describe quadrilaterals?

Quadrilaterals are named by their sides and their angles.

quadrilateral

__ sides

__ angles

trapezoid

exactly __ pair of opposite sides that are parallel

lengths of sides could be the same

rectangle

_ pairs of opposite sides that are parallel

_ pairs of sides that are of equal length

_ right angles

square

_ pairs of opposite sides that are parallel

_ sides that are of equal length

_ right angles

rhombus

_ pairs of opposite sides that are parallel

_ sides that are of equal length

Chapter 12 501

Explain why a square can also be named a rectangle or a rhombus.

Lesson 12.5

Describe quadrilaterals.

MATHEMATICAL PRACTICES

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502

4.

rectangle

rhombus

square

trapezoid

5.

rhombus

quadrilateral

square

rectangle

6.

rectangle

rhombus

trapezoid

quadrilateral

On Your OwnnCircle all the words that describe the quadrilateral. 7.

rectangle

trapezoid

quadrilateral

rhombus

8.

rectangle

rhombus

trapezoid

square

9.

quadrilateral

square

rectangle

rhombus

Share and ShowLook at the quadrilateral at the right.

1. Outline each pair of opposite sides that are parallel with a different color. How many pairs of opposite

sides appear to be parallel? __

2. Look at the parallel sides you colored.

The sides in each pair are of __ length.

3. Name the quadrilateral. ____

Circle all the words that describe the quadrilateral.

Explain how you can have a rhombus that is not a square.

Think: All the angles are right angles.

AB C

F

ED

AB C

F

ED

AB C

F

ED

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10. Which quadrilaterals appear to have 4 right angles?

11. Which quadrilaterals appear to have 2 pairs of opposite sides that are parallel?

12. Which quadrilaterals appear to have no right angles?

Problem SolvingUse the quadrilaterals at the right for 10–12.

13. The opposite sides of _ rectangles are parallel.

15. _ squares are rectangles.

17. _ quadrilaterals are polygons.

14. _ sides of a rhombus are the same length.

16. _ rhombuses are squares.

18. _ polygons are quadrilaterals.

Write all or some to complete the sentence for 13–18.

19. Circle the shape at the right that is not a quadrilateral. Explain your choice.

20. I am a polygon that has 4 sides and 4 angles. At least one of my angles is less than a right angle. Circle all the shapes that I could be.

quadrilateral rectangle square rhombus trapezoid

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504 FOR MORE PRACTICE:Standards Practice Book, pp. P247–P248

21. Test Prep Rita glued craft sticks together to make this shape. Which best describes the quadrilateral Rita made?

A square B rectangle C rhombus D trapezoid

Compare and ContrastWhen you compare, you look for ways that things are alike. When you contrast, you look for ways that things are different.

Mr. Briggs drew some shapes on the board. He asked the class to tell how the shapes are alike and how they are different.

Complete the sentences.

t� �4IBQFT�_ , _ , _ , _ , _ , _ , and _ are polygons.

t� �4IBQFT�_ , _ , and _ are not polygons.

t� �4IBQFT�_ , _ , _ , and _ are quadrilaterals.

t� �4IBQFT�_ , _ , and _ appear to have only 1 pair of opposite sides that are parallel.

t� �4IBQFT�_ , _ , and _ appear to have 2 pairs of opposite sides that are parallel.

t� �"MM���TJEFT�PG�TIBQFT�_ and _ appear to be the same length.

t� �*O�UIFTF�QPMZHPOT �BMM�TJEFT�EP�not appear to be the same length. ____

t� 5IFTF�TIBQFT�DBO�CF�DBMMFE�SIPNCVTFT��____

t� 4IBQFT�_ and _ are quadrilaterals, but cannot be called rhombuses.

t� 4IBQF�_ is a rhombus and can be called a square.

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Lesson 12.5

Classify Quadrilaterals

Circle all the words that describe the quadrilateral.

Use the quadrilaterals below for 4–6.

7. A picture on the wall in Jeremy’s classroom has 4 right angles, 4 sides of equal length, and 2 pairs of opposite sides that are parallel. What quadrilateral best describes the picture?

8. Sofia has a plate that has 4 sides of equal length, 2 pairs of opposite sides that are parallel, and no right angles. What quadrilateral best describes the plate?

Chapter 12 P247

1.

square

rectangle

rhombus

trapezoid

2.

square

rectangle

rhombus

trapezoid

3.

square

rectangle

rhombus

trapezoid

4. Which quadrilaterals appear to have no right angles?

5. Which quadrilaterals appear to have 4 right angles?

6. Which quadrilaterals appear to have 4 sides of equal length?

COMMON CORE STANDARD MACC.3.G.1.1

Reason with shapes and their attributes.

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P248

Lesson Check (MACC.3.G.1.1)

1. Which word describes the quadrilateral?

A square

B trapezoid

C rhombus

D rectangle

2. Which quadrilaterals appear to have 2 pairs of opposite sides that are parallel?

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A A and B

B A, B, and C

C A only

D B only

Spiral Review (MACC.3.G.1.1)

5. What word describes the dashed sides of the shape shown? (Lesson 12.4)

A intersecting C perpendicular

B parallel D right

6. How many right angles does this shape have? (Lesson 12.2)

A 0 C 2

B 1 D 3

3. Aiden drew the the polygon shown. What is the name of the polygon he drew? (Lesson 12.3)

A decagon C octagon

B hexagon D pentagon

4. How many pairs of parallel sides does this shape appear to have? (Lesson 12.4)

A 4 C 1

B 2 D 0