Topic 15 Classifying Plane Figures

Transcription

1 Topic 15 Classifying Plane Figures Name Test Date

2 Topic 15 Vocabulary Cards polygon polygon A closed plane figure made up of line segments regular polygon Fold here regular polygon A polygon that has sides of equal length and angles of equal measure A polygon with 3 sides Topic 15 1 of 7

3 quadrilateral quadrilateral A polygon with 4 sides pentagon Fold here pentagon A polygon with 5 sides hexagon hexagon A polygon with 6 sides Topic 15 2 of 7

4 octagon octagon A polygon with 8 sides equilateral Fold here equilateral A whose sides all have the same length isosceles isosceles A with two sides of the same length Topic 15 3 of 7

5 scalene scalene A in which no sides have the same length right Fold here right A in which one angle is a right angle acute acute A whose angles are all acute angles Topic 15 4 of 7

6 obtuse obtuse A in which one angle is an obtuse angle parallelogram Fold here parallelogram A quadrilateral with both pairs of opposite sides parallel trapezoid trapezoid A quadrilateral that has exactly one pair of parallel sides Topic 15 5 of 7

7 rectangle rectangle A parallelogram with four right angles rhombus Fold here rhombus A parallelogram with all sides the same length square square A rectangle with all sides the same length Topic 15 6 of 7

8 generalization generalization A general statement Example: A generalization about rectangles applies to all rectangles. Fold here Topic 15 7 of 7

9 1. The table shows the cost of a yard service based on the amount of time the service spends on a yard. Hours Cost ($) Which expression tells the amount the service charges for h hours of work? A 6h C h 6 B 15h D h What would be the services charge for 18 hours of work? A $30 C $108 B $90 D $ A copy machine can make 742 copies in 53 minutes. How many copies can the machine make in 1 minute? Daily Common Core Review 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 F during the first hour. 10 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 By Friday, the price was By how much did the price change from Monday to Friday? A 11 C 104 B 14 D 114 D 15 1

10 Polygons Classify each polygon. Then tell if it appears to be a regular or irregular polygon Practice Classify the polygon. Name the vertices. H T B E 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

11 Quick Check How many vertices does an octagon have? A 6 B 7 C 8 D 9 2. Which best describes the polygon? A a regular B a regular quadrilateral C an irregular D an irregular quadrilateral 3. Writing to Explain 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

12 1. The shape below is a regular octagon. Which must be true about the measure of ABC? Daily Common Core Review Draw an irregular hexagon. A B H G C D F E 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? W A Hexagon B Pentagon C Quadrilateral D Triangle Y X Z 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 Bagels Biscuits Pizza crust Rolls Flour (cups) List the breads in order from the one using the most to the least flour. D 15 2

13 Triangles Classify each by its sides and then by its angles ft 4 m 4 m 9.5 ft Practice ft 60 4 m 60 Given the measures of the angles for a, classify the by angles , 62, , 90, , 75, º, 36, Judy bought a new tent for a camping trip. Look at the side of the tent with the opening to classify the by its sides and its angles. 4 ft 3 ft 4 ft 8. Which describes a scalene? A 4 equal sides B 3 equal sides C 2 equal sides D 0 equal sides 9. The lengths of two sides of a are 15 in. each. The third side measures 10 in. What type of is this? Explain your answer using geometric terms. P 15 2

14 1. Which terms describe this? Quick Check Molly needs to classfy the below based on angles. Which class is correct? 60 A equilateral, acute B scalene, acute C scalene, obtuse D isosceles, obtuse A Acute B Isosceles C Equilateral D Obtuse 3. In a PQR, PQ 5 2 ft, QR 5 2 ft, and PR 5 2 ft. Classify the. A equilateral, acute B scalene, obtuse C isosceles, acute D isosceles, right 4. Writing to Explain Derek is building the triangular flower bed shown below. Classify the. Explain Q 15 2

15 1. The map shows three streets that intersect to form a. Big Avenue Main Street Pecan Road Big Avenue and Pecan Road make a 130 angle. The angle of Pecan Road and Main Street is 20. What kind of is this? A Obtuse B Acute C Right D Equilateral 2. Nina draws a closed shape with 5 sides. What did she draw? A Hexagon B Nonagon C Octagon D Pentagon cm 45 cm cm Daily Common Core Review Circle two words from the list below that tell what kind of this is. acute isosceles right equilateral obtuse scalene 5. Jessie uses 4 _ 2 square yards of 4 cloth to make a choir robe. Write 4 _ 2 as an improper fraction in 4 simplest form. 6. Draw a factor tree to show the prime factors of 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 D 15 3

16 Attributes of Quadrilaterals Classify each quadrilateral. Be as specific as possible. Practice cm cm 18 cm 18 cm 8 cm 8 cm 20 cm 15 cm 3. 8 in cm 4 in. 4 in. 17 cm 17 cm 8 in. 17 cm 5. Name the vertices of the square to the right. F G 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? L A 7. Can a trapezoid have four obtuse angles? Explain. P 15 3

17 1. Which best classifies the quadrilateral? A square B rhombus C rectangle D trapezoid Quick Check The angles of a quadrilateral have the following measures: 90, 90, 125, and 55. Classify the quadrilateral by angles. A rectangle B square C trapezoid D rhombus 3. Which of the following four quadrilaterals is NOT a parallelogram? A square B rhombus C trapezoid D rectangle 4. Writing to Explain A new swimming pool is in the shape of the quadrilateral shown below a. Classify the quadrilateral. Explain. Q 15 3

18 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 B x 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 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? Daily Common Core Review 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. A 10y B 10 + y C 10 y D 10 y D 15 4

19 Special Quadrilaterals Practice 15-4 In 1 6, classify each polygon in as many ways as possible 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, Writing to Explain What attributes help you tell the difference between a rhombus and a rectangle? Explain. P 15 4

20 Quick Check What type of quadrilateral is shown below? A Rectangle B Trapezoid C Rhombus D Square 2. What is true about every rhombus? A All angles are equal. B All sides are equal. C Exactly one pair of sides is parallel. D No pairs of sides are parallel. 3. Writing to Explain Draw a quadrilateral with 4 equal sides and 4 right angles. What type of special quadrilateral did you draw? What are 3 more names for that special quadrilateral? Q 15 4

21 1. The drawing shows a shelf from a corner bookcase. What is the area of the shelf? 8 in. Daily Common Core Review 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. 6 in. A 2 in 2 B 24 in 2 C 48 in 2 D 96 in 2 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, Write >, <, or = in the blank to make the number sentence true _ 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. 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 D 15 5

22 Classifying Quadrilaterals In 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. Practice 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, 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

23 1. Which quadrilateral is NOT a parallelogram? A square B trapezoid C rhombus D rectangle Quick Check How are a rhombus and a square alike? A Both have equal angles. B Both have equal sides. C Both have exactly one pair of parallel sides. D Neither have any sets of parallel sides. 3. How are a parallelogram and a trapezoid different? A A parallelogram has only 1 pair of parallel sides, but a trapezoid has 2. B A trapezoid has only 1 pair of parallel sides, but a parallelogram has 2. C A trapezoid has 4 right angles, but a parallelogram doesn t need to have 4 right angles. D A parallelogram has 4 right angles, but a trapezoid doesn t need to have 4 right angles. 4. Writing to Explain Draw a quadrilateral that is both a rectangle and a rhombus. What type of special quadrilateral did you draw? Q 15 5

24 1. The drawing shows a school playground. west north east Daily Common Core Review 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? south 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 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? 2. In this parallelogram S and Q have the same measure. What is the measure of Q? P Q S R D 15 6

25 Problem Solving: Make and Test Generalizations In 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 s have right angles. Practice All rectangles have right angles. 3. Any two s 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 How can you show that a generalization is likely correct? P 15 6

26 Quick Check 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 Writing to Explain Read the generalization: All odd numbers greater than 30 are divisible by 3. How can 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