topic 15 classifying plane figures · pdf filecopyright © pearson education, inc., or its...

Topic 15

Classifying Plane Figures

___________________

Name

___________________

Test Date

Name

Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5

Topic 15

Vocabulary Cards

polygon

regular polygon

triangle

polygon

A closed plane figure made up of line segments

regular polygon

A polygon that has sides of equal length and angles

of equal measure

triangle

A polygon with 3 sides

Fold

her

e

1 of 7Topic 15

Name


quadrilateral

pentagon

hexagon

quadrilateral


pentagon


hexagon


Fold

her

e

2 of 7Topic 15

Name


octagon

equilateral triangle

isosceles triangle

octagon


equilateral triangle

A triangle whose sides all have the same length

isosceles triangle

A triangle with two sides of the same length

Fold

her

e

3 of 7Topic 15

Name


scalene triangle

right triangle

acute triangle

scalene triangle

A triangle in which no sides have the

same length

right triangle

A triangle in which one angle is a right angle

acute triangle

A triangle whose angles are all acute angles

Fold

her

eFo

ld h

ere

4 of 7Topic 15

Name


obtuse triangle

parallelogram

trapezoid

obtuse triangle

A triangle in which one angle is an obtuse angle

parallelogram

A quadrilateral with both pairs of opposite

sides parallel

trapezoid

A quadrilateral that has exactly one pair of

parallel sides

Fold

her

eFo

ld h

ere

5 of 7Topic 15

Name


rectangle

rhombus

square

rectangle

A parallelogram with four right angles

rhombus

A parallelogram with all sides the same length

square

A rectangle with all sides the same length

Fold

her

e

6 of 7Topic 15

Name


generalization

generalization

A general statement Example: A generalization about rectangles applies

to all rectangles.

Fold

her

e

7 of 7Topic 15

Name


Daily Common Core Review15-1

1. The table shows the cost of a yard service based on the amount of time the service spends on a yard.

Hours Cost($)3 184 246 368 48

Which expression tells the amount the service charges for h hours of work?

A 6h C h 6

B 15h D h 15

2. What would be the services charge for 18 hours of work?

A $30 C $108

B $90 D $180

3. A copy machine can make 742 copies in 53 minutes. How many copies can the machine make in 1 minute?

A 11 C 104

B 14 D 114

4. Riley walked 10 1 _ 2 miles in 2 3 _ 4 hours. At this speed how far does Riley walk in one hour?

5. In a science experiment, the temperature of a sample increased 2 __ 10 ̊F during the first hour. At the end of the second hour, the temperature increased another 6 __ 10 ̊F. What was the total temperature increase for the two hours? Write your answer in simplest form.

6. On Monday, the price of one share of Webb Company stock was 24.85. By Friday, the price was 25.004. By how much did the price change from Monday to Friday?

D 15•1

E

H

TB

Name


Practice

15-1PolygonsClassify each polygon. Then tell if it appears to be a regular or irregular polygon.

1. 2.

3. Classify the polygon. Name the vertices.

4. Which polygon has eight sides?

A quadrilateral B pentagon C hexagon D octagon

5. Writing to Explain Draw two regular polygons and two that are irregular. Use geometric terms to describe one characteristic of each type.

P 15•1

Name


Quick Check

15-1

1. How many vertices does an octagon have?

A 6

B 7

C 8

D 9

2. Which best describes the polygon?

A a regular triangle

B a regular quadrilateral

C an irregular triangle

D an irregular quadrilateral

3. WritingtoExplain Anna is building a flower garden in the shape at the right.

a. Name the polygon.

b. How many sides and vertices does the polygon have?

c. If one side of the garden is 5 ft, what is the perimeter of the garden?

d. All the angles of the polygon are equal. If the total measure of the angles is 540˚, how many degrees is each angle of the polygon?

Q 15•1

W X

Y Z

A B

C

D

EF

G

H

Name



1. The shape below is a regular octagon. Which must be true about the measure of ABC?

A It must equal the sum of ___

AB 1 ___

BC. B It must equal the sum of

___

GF 1 ___

FE.C It must equal the measure

of ACE.

D It must equal the measure of GFE.

2. What type of polygon is formed by the points below?

A Hexagon

B Pentagon

C Quadrilateral

D Triangle

3. Draw an irregular hexagon.

4. Ms. Wilson shows her cooking class how to make four different kinds of bread. The table shows the amount of flour for each.

Bread Flour(cups)

Bagels 3 1 __ 3

Biscuits 2 3 __ 4

Pizza crust 3 2 __ 3

Rolls 3 1 __ 2

Listthe breads in order from the one using the most to the least flour.

D 15•2

8 ft

12.42 ft 9.5 ft

4 m

4 m4 m60�

60� 60�

4 ft4 ft

3 ft

Name


Practice

15-2TrianglesClassify each triangle by its sides and then by its angles.

1. 2.

Given the measures of the angles for a triangle, classify the triangle by angles.

3. 47°, 62°, 71° 4. 29°, 90°, 61°

5. 75°, 75°, 30° 6. 54º, 36°, 90°

7. Judy bought a new tent for a camping trip. Look at the side of the tent with the opening to classify the triangle by its sides and its angles.

8. Which describes a scalene triangle?

A 4 equal sides B 3 equal sides C 2 equal sides D 0 equal sides

9. The lengths of two sides of a triangle are 15 in. each. The third side measures 10 in. What type of triangle is this? Explain your answer using geometric terms.

P 15•2

60°

50° 70°

90°

50°

40°


Quick Check

15-2Name

1. Which terms describe this triangle?

A equilateral, acute

B scalene, acute

C scalene, obtuse

D isosceles, obtuse

2. Molly needs to classfy the triangle below based on angles. Which class is correct?

A Acute triangle

B Isosceles triangle

C Equilateral triangle

D Obtuse triangle

3. In a triangle ∆PQR, ___

 PQ  5 2 ft, ___

QR 5 2 ft, and ___

PR  5 2 ft. Classify the triangle.

A equilateral, acute

B scalene, obtuse

C isosceles, acute

D isosceles, right

4. WritingtoExplain Derek is building the triangular flower bed shown below. Classify the triangle. Explain.

Q 15•2

Main Street

Big Avenue Pecan Road

45 cm 45 cm

60 cm52° 52°

76°

Name



1. The map shows three streets that intersect to form a triangle.

BigAvenue and Pecan Road make a 130° angle. The angle of Pecan Road and Main Street is 20°. What kind of triangle is this?

A Obtuse triangle

B Acute triangle

C Right triangle

D Equilateral triangle

2. Nina draws a closed shape with 5 sides. What did she draw?

A Hexagon

B Nonagon

C Octagon

D Pentagon

3. Consuela is 7 inches taller than Erin. Let e be Erin’s height. Which expression tells Consuela’s height?

A e 2 7

B e 1 7

C 7 2 e

D 7 3 e

4. Circle two words from the list below that tell what kind of triangle this is.

acute equilateral

isosceles obtuse

right scalene

5. Jessie uses 4 2 _4 square yards of cloth to make a choir robe. Write 4 2 _ 4 as an improper fraction in simplest form.

6. Draw a factor tree to show the prime factors of 40.

D 15•3

6 cm

18 cm

20 cm

18 cm 8 cm 8 cm

15 cm

15 cm

8 in.

8 in.

4 in.4 in.

17 cm

17 cm

17 cm 17 cm

GF

AL

Name


Practice

15-3Attributes of QuadrilateralsClassify each quadrilateral. Be as specific as possible.

1. 2.

3. 4.

5. Name the vertices of the square to the right.

6. The angles of a quadrilateral measure 80°, 100°, 100° and 80° in this order. What kind of quadrilateral has this shape? What attributes help you solve the problem?

7. Can a trapezoid have four obtuse angles? Explain.

P 15•3

65�65�

115�115�

Name


Quick Check

15-3

3. WhichofthefollowingfourquadrilateralsisNOTaparallelogram?

A square

B rhombus

C trapezoid

D rectangle

4. WritingtoExplain Anewswimmingpoolisintheshapeofthequadrilateralshownbelow.

a. Classifythequadrilateral.Explain.

1. Whichbestclassifiesthequadrilateral?

A square

B rhombus

C rectangle

D trapezoid

2. Theanglesofaquadrilateralhavethefollowingmeasures:90°,90°,125°,and55°.Classifythequadrilateralbyangles.

A rectangle

B square

C trapezoid

D rhombus

Q 15•3

Name



1. Tom and Lisa each buy 3 pairs of pants. Tom spends $5 less than Lisa spends. Let x be the amount that Tom spends. Which shows Lisa’s spending?

A x + 5 – 3

B x – 3 + 5

C x + 5

D x – 5

2. A restaurant has 189 pounds of hamburger in the kitchen. A family-sized special meal uses 3 pounds of hamburger. How many family-sized special meals can the restaurant make?

A 61

B 62

C 63

D 64

3. Molly travels 10 miles for every hour she bikes. Which expression tells how many miles Molly can go if she rides her bicycle for y hours?

A 10y

B 10 + y

C 10 – y

D 10 ÷ y

4. A hotel charges $119 per night for a room, including tax. What is the cost of the room for 4 nights?

5. A school has 1,053 students. During each of the school’s nine periods, the same number of students have physical education. How many students have physical education during one period?

6. Elisa buys a 60-pound bag of cat food.

a. Write an expression that tells how many weeks the bag will last if Elisa’s cat eats x pounds of food each week.

b. If the cat eats 3 pounds of food each week, will the bag last for 21 weeks? Explain.

D 15•4

Name


Practice

15-4Special QuadrilateralsIn 1–6, classify each polygon in as many ways as possible.

1.

2.

3.

4.

5.

6.

7. Draw a quadrilateral with 1 pair of parallel sides. What special quadrilateral have you drawn?

8. A parallelogram has one side that is 7 inches and one side that is 11 inches. What is the perimeter of the parallelogram?

9. Which shows the most likely side lengths for a parallelogram?

A 2, 2, 6, 2 B 2, 6, 2, 6 C 2, 2, 3, 6 D 2, 6, 6, 6

10. Writing to Explain What attributes help you tell the difference between a rhombus and a rectangle? Explain.

P 15•4

Name


Quick Check

15-4

1. Whattypeofquadrilateralisshownbelow?

A Rectangle

B Trapezoid

C Rhombus

D Square

2. Whatistrueabouteveryrhombus?

A Allanglesareequal.

B Allsidesareequal.

C Exactlyonepairofsidesisparallel.

D Nopairsofsidesareparallel.

3. WritingtoExplain Drawaquadrilateralwith4equalsidesand4rightangles.Whattypeofspecialquadrilateraldidyoudraw?Whatare3morenamesforthatspecialquadrilateral?

Q 15•4

Name



1. The drawing shows a shelf from a corner bookcase.

What is the area of the shelf?

A 2 in2

B 24 in2

C 48 in2

D 96 in2

2. Molly, Nathan, and Sam own a bookstore. They agree to share the profit equally. If the profit is $8,822, which is the best estimate of each owner’s share?

A $2,000

B $3,000

C $4,000

D $5,000

3. Jane buys a set of 17 spiral notebooks. Each notebook has 95 pages. What is the total number of pages?

A 1,615

B 1,605

C 615

D 605

4. There are sixteen children in a juggling class. Ten of them have learned to juggle 4 balls at a time. What fraction of them have learned to juggle 4 balls at a time? Write your answer in simplest form.

5. Write >, <, or = in the blank to make the number sentence true.

11 __ 16 3 _ 4

6. A rectangular rug is x feet long and y feet wide, with a perimeter of 60 feet. Both x and y are whole numbers between 10 and 20 feet. Fill in the blanks to complete the sentence.

The area of the rug is greater than

but less than

.

8 in

.

6 in.

D 15•5

Name


Practice

15-5Classifying QuadrilateralsIn 1–8, tell whether each statement is true or false. Remember, for a statement to be true is has to be true in EVERY circumstance.

1. A rectangle is a quadrilateral.

2. All parallelograms are trapezoids.

3. A quadrilateral is a square.

4. A quadrilateral is a trapezoid.

5. A rhombus is a rectangle.

6. A trapezoid is a parallelogram.

7. A square is a rectangle.

8. A rectangle is a quadrilateral.

9. Which shows the most likely side lengths for a parallelogram?

A 9, 4, 9, 4 B 9, 9, 9, 4 C 4, 4, 4, 9 D 4, 9, 9, 6

10. Draw 3 different quadrilaterals with 2 pairs of parallel sides. What are the names of the special quadrilaterals you have drawn?

11. A parallelogram has one side that is 9 millimeters and one side that is 13 millimeters. What is the perimeter of the parallelogram?

12. Writing to Explain What characteristics help you tell the difference between a parallelogram and a trapezoid? Explain.

P 15•5

Name


Quick Check

15-5

1. WhichquadrilateralisNOTaparallelogram?

A square

B trapezoid

C rhombus

D rectangle

2. Howarearhombusandasquarealike?

A Bothhaveequalangles.

B Bothhaveequalsides.

C Bothhaveexactlyonepairofparallelsides.

D Neitherhaveanysetsofparallelsides.

4. WritingtoExplain Drawaquadrilateralthatisbotharectangleandarhombus.Whattypeofspecialquadrilateraldidyoudraw?

3. Howareaparallelogramandatrapezoiddifferent?

A Aparallelogramhasonly1pairofparallelsides,butatrapezoidhas2.

B Atrapezoidhasonly1pairofparallelsides,butaparallelogramhas2.

C Atrapezoidhas4rightangles,butaparallelogramdoesn’tneedtohave4 rightangles.

D Aparallelogramhas4rightangles,butatrapezoiddoesn’tneedtohave4 rightangles.

Q 15•5

north

south

eastwest

S

P

R

Q

105�

105�

Name



1. The drawing shows a school playground.

The north and south sides of the playground are parallel, but the east and west sides are NOT parallel. What is the shape of the playground?

A Square

B Rhombus

C Trapezoid

D Parallelogram

2. In this parallelogram S and Q have the same measure. What is the measure of Q?

3. A computer room has 12 computers. The room is open for 4 hours each day. Twenty-five students sign up for computer time. Each student gets the same number of minutes. What is the greatest whole number of minutes each student can get?

4. At a track meet, Travis jumps 1.03 meters in the high jump. Andrew jumps 1.32 meters. How much higher does Andrew jump?

5. A book has 84 pages. Each page has an average of 437 words. How many words are in the book?

D 15•6

Name


Practice

15-6Problem Solving: Make and Test GeneralizationsIn 1 through 5, test the generalization and state whether it appears to be correct or incorrect. If incorrect, give an example to support why.

1. All triangles have right angles.

2. All rectangles have right angles.

3. Any two triangles can be joined to make a rhombus.

4. All rectangles can be cut in half vertically or horizontally to make two smaller rectangles that are the same size and same shape.

5. Intersecting lines are also parallel.

6. How many whole numbers have exactly three digits?Hint: 999 is the greatest whole number with three digits.

A 890 B 900 C 990 D 999

7. How can you show that a generalization is likely correct?

P 15•6

Name


Quick Check

15-6

1. Which of these generalizations is true?

A All rectangles are squares.

B All parallelograms are rectangles.

C All squares are parallelograms.

D All trapezoids are parallelograms.

2. Which generalization can be shown to be incorrect based on the illustration below?

A Rectangular prisms have 8 vertices.

B All rectangular prisms are cubes.

C Triangular prisms have 6 vertices.

D All cubes are rectangular prisms.

3. Lisa looked at a group of even numbers. The numbers were 4, 8, 48, and 64. She made a generalization that all even numbers can be divided by 4. Which number below could you use to show whether Lisa’s generalization is correct or incorrect?

A 18 B 28 C 60 D 100

4. WritingtoExplain Read the generalization:

All odd numbers greater than 30 are divisible by 3.

Howcan you test this generalization to determine whether it is correct or incorrect? Explain what test you can use and then determine whether the generalization is correct.

Q 15•6

topic 15 classifying plane figures · pdf filecopyright © pearson education, inc., or its...

Documents