Fair Game Review. Chapter 7 A B C D E Name Date. Complete the number sentence with <, >, or =

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1 Name Date Chapter 7 Fair Game Review Complete the number entence with <, >, or = Find three decimal that make the number entence true > < 9. The table how the time of a 100-meter dah. Order the runner from firt place to fifth place. Runner Time (econd) A B C D E Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 141

2 Name Date Chapter 7 Fair Game Review (continued) Evaluate the expreion ( ) The table how the number of tudent in 4 clae. The teacher are combining the clae and dividing the tudent in half to form two group for a project. Write an expreion to repreent thi ituation. How many tudent are in each group? Cla Student Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

3 Name Date 7.1 Finding Square Root For ue with Activity 7.1 Eential Quetion How can you find the dimenion of a quare or a circle when you are given it area? When you multiply a number by itelf, you quare the number. Symbol for quaring i the exponent = 4 4 = 16 4 quared i 16. To undo thi, take the quare root of the number. Symbol for quare root i a radical ign, = 4 = 4 The quare root of 16 i 4. 1 ACTIVITY: Finding Square Root Work with a partner. Ue a quare root ymbol to write the ide length of the quare. Then find the quare root. Check your anwer by multiplying. a. Sample: = 121 = Check: Area = 121 ft 2 The length of each ide of the quare i. b. Area = 81 yd 2 c. Area = 324 cm 2 d. Area = 361 mi 2 Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 143

Name Date 7.1 Finding Square Root (continued) e. Area = 225 mi 2 f. Area = 2.89 in. 2 g. 4 Area = ft 9 2 2 ACTIVITY: Uing Square Root Work with a partner.

25π ft 2 9 Area = m 16 p 2 3 ACTIVITY: The Period of a Pendulum Work with a partner.

4 Name Date 7.1 Finding Square Root (continued) e. Area = 225 mi 2 f. Area = 2.89 in. 2 g. 4 Area = ft ACTIVITY: Uing Square Root Work with a partner. Find the radiu of each circle. a. b. r r Area = 36π in. 2 Area = π yd 2 c. d. r r Area = 0.25π ft 2 9 Area = m 16 p 2 3 ACTIVITY: The Period of a Pendulum Work with a partner. The period of a pendulum i the time (in econd) it take the pendulum to wing back and forth. The period T i repreented by T = 1.1 L, where L i the length of the pendulum (in feet). L Complete the table. Then graph the function on the next page. I the function linear? 144 Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

5 Name Date 7.1 Finding Square Root (continued) L T T 8 Period of a Pendulum 7 6 Period (econd) L Length (feet) What I Your Anwer? 4. IN YOUR OWN WORDS How can you find the dimenion of a quare or circle when you are given it area? Give an example of each. How can you check your anwer? Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 145

6 Name Date 7.1 Practice For ue after Leon 7.1 Find the two quare root of the number Find the quare root() Evaluate the expreion A trampoline ha an area of 49π quare feet. What i the diameter of the trampoline? 146 Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

7 Name Date 7.2 Finding Cube Root For ue with Activity 7.2 Eential Quetion How i the cube root of a number different from the quare root of a number? When you multiply a number by itelf twice, you cube the number. Symbol for cubing i the exponent = = 64 4 cubed i 64. To undo thi, take the cube root of the number. Symbol for cube root i = 4 = 4 The cube root of 64 i 4. 1 ACTIVITY: Finding Cube Root Work with a partner. Ue a cube root ymbol to write the edge length of the cube. Then find the cube root. Check your anwer by multiplying. a. Sample: = 343 = 7 = 7 inche Volume = 343 in. 3 Check = 49 7 = 343 The edge length of the cube i 7 inche. b. Volume = 27 ft 3 c. Volume = 125 m 3 Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 147

8 Name Date 7.2 Finding Cube Root (continued) d. Volume = cm 3 e. 1 Volume = yd ACTIVITY: Ue Prime Factorization to Find Cube Root Work with a partner. Write the prime factorization of each number. Then ue the prime factorization to find the cube root of the number. a = ( 3 ) ( 3 ) ( 3 ) = = Prime factorization Commutative Property of Multiplication Simplify. The cube root of 216 i. b c Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

9 Name Date 7.2 Finding Cube Root (continued) d. STRUCTURE Doe thi procedure work for every number? Explain why or why not. What I Your Anwer? 3. Complete each tatement uing poitive or negative. a. A poitive number time a poitive number i a number. b. A negative number time a negative number i a number. c. A poitive number multiplied by itelf twice i a number. d. A negative number multiplied by itelf twice i a number. 4. REASONING Can a negative number have a cube root? Give an example to upport your explanation. 5. IN YOUR OWN WORDS How i the cube root of a number different from the quare root of a number? 6. Give an example of a number whoe quare root and cube root are equal. 7. A cube ha a volume of 13,824 cubic meter. Ue a calculator to find the edge length. Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 149

10 Name Date 7.2 Practice For ue after Leon 7.2 Find the cube root Evaluate the expreion ( 12) The volume of a cube i 1000 cubic inche. What i the edge length of the cube? 150 Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

So, the rule that Pythagora dicovered i called the Pythagorean Theorem. Pythagora (c. 570 c. 490 B.C.) 1 ACTIVITY: Dicovering the Pythagorean Theorem Work with a

11 Name Date 7.3 The Pythagorean Theorem For ue with Activity 7.3 Eential Quetion How are the length of the ide of a right triangle related? Pythagora wa a Greek mathematician and philoopher who dicovered one of the mot famou rule in mathematic. In mathematic, a rule i called a theorem. So, the rule that Pythagora dicovered i called the Pythagorean Theorem. Pythagora (c. 570 c. 490 B.C.) 1 ACTIVITY: Dicovering the Pythagorean Theorem Work with a partner. a. On grid paper, draw any right triangle. Label the length of the two horter ide a and b. c 2 b. Label the length of the longet ide c. c. Draw quare along each of the three ide. Label the area of the three quare a 2, b 2, and c 2. c b a b 2 a 2 d. Cut out the three quare. Make eight copie of the right triangle and cut them out. Arrange the figure to form two identical larger quare. a 2 e. MODELING The Pythagorean Theorem decribe the relationhip among a 2, b 2, and c 2. Ue your reult from part (d) to write an equation that decribe thi relationhip. c 2 b 2 Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 151

12 Name Date 7.3 The Pythagorean Theorem (continued) 2 ACTIVITY: Uing the Pythagorean Theorem in Two Dimenion Work with a partner. Ue a ruler to meaure the longet ide of each right triangle. Verify the reult of Activity 1 for each right triangle. a. b. 2 cm 4 cm 4.8 cm 3 cm c. d. 1 1 in. 4 1 in in. 2 in. 152 Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

13 Name Date 7.3 The Pythagorean Theorem (continued) 3 ACTIVITY: Uing the Pythagorean Theorem in Three Dimenion Work with a partner. A guy wire attached 24 feet above ground level on a telephone pole provide upport for the pole. a. PROBLEM SOLVING Decribe a procedure that you could ue to find the length of the guy wire without directly meauring the wire. guy wire b. Find the length of the wire when it meet the ground 10 feet from the bae of the pole. What I Your Anwer? 4. IN YOUR OWN WORDS How are the length of the ide of a right triangle related? Give an example uing whole number. Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 153

14 Name Date 7.3 Practice For ue after Leon 7.3 Find the miing length of the triangle c b a 4.8 Find the miing length of the figure. 4. x 5. x 13 m 63 cm 16 cm 35 m 5 m 6. In wood hop, you make a bookend that i in the hape of a right triangle. What i the bae b of the bookend? 8 in. 10 in. b 154 Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

15 Name Date 7.4 Approximating Square Root For ue with Activity 7.4 Eential Quetion How can you find decimal approximation of quare root that are not rational? 1 ACTIVITY: Approximating Square Root Work with a partner. Archimede wa a Greek mathematician, phyicit, engineer, inventor, and atronomer. He tried to find a rational number whoe quare i 3. Two that he tried were and a. Are either of thee number equal to 3? Explain. b. Ue a calculator to approximate 3. Write the number on a piece of paper. Enter it into the calculator and quare it. Then ubtract 3. Do you get 0? What doe thi mean? c. The value of 3 i between which two integer? d. Tell whether the value of 3 i between the given number. Explain your reaoning. 1.7 and and and ACTIVITY: Approximating Square Root Geometrically Work with a partner. Refer to the quare on the number line below a. What i the length of the diagonal of the quare? b. Copy the quare and it diagonal onto a piece of tranparent paper. Rotate it about zero on the number line o that the diagonal align with the number line. Ue the number line to etimate the length of the diagonal. Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 155

Name Date 7.4 Approximating Square Root (continued) c. STRUCTURE How do you think your anwer in part (a) and (b) are related? 3 ACTIVITY: Approximating Square Root Geometrically Work with a partner.

Draw your egment near the left edge of the grid. Label thi egment DC. c. Set the point of a compa on A. d. Ue the Pythagorean Theorem to Set the compa to 2 unit. Swing find the length of egment BC.

16 Name Date 7.4 Approximating Square Root (continued) c. STRUCTURE How do you think your anwer in part (a) and (b) are related? 3 ACTIVITY: Approximating Square Root Geometrically Work with a partner. a. Ue grid paper and the given cale to draw a horizontal line egment 1 unit in length. Draw your egment near the bottom of the grid. Label thi egment AC. b. Draw a vertical line egment 2 unit in length. Draw your egment near the left edge of the grid. Label thi egment DC. c. Set the point of a compa on A. d. Ue the Pythagorean Theorem to Set the compa to 2 unit. Swing find the length of egment BC. the compa to interect egment DC. Label thi interection a B. Scale: 1 of a unit 10 e. Ue the grid paper to approximate 3 to the nearet tenth. 156 Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

17 Name Date 7.4 Approximating Square Root (continued) 4. Compare your approximation in Activity 3 with your reult from Activity 1. What I Your Anwer? 5. Repeat Activity 3 for a triangle in which egment AC i 2 unit and egment BA i 3 unit. Ue the Pythagorean Theorem to find the length of egment BC. Ue the grid paper to approximate 5 to the nearet tenth. Scale: 1 of a unit IN YOUR OWN WORDS How can you find decimal approximation of quare root that are not rational? Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 157

18 Name Date 7.4 Practice For ue after Leon 7.4 Claify the real number Etimate the quare root to the nearet (a) integer and (b) tenth Which number i greater? Explain , , , The velocity in meter per econd of a ball that i dropped from a window at a height of 10.5 meter i repreented by the equation v = ( )( ) Etimate the velocity of the ball. Round your anwer to the nearet tenth. 158 Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

19 Name Date Extenion 7.4 Practice For ue after Extenion 7.4 Write the decimal a a fraction or a mixed number Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 159

20 Name Date Extenion 7.4 Practice (continued) The length of a pencil i 1.56 inche. Repreent the length of the pencil a a mixed number. 160 Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

21 Name Date 7.5 Uing the Pythagorean Theorem For ue with Activity 7.5 Eential Quetion In what other way can you ue the Pythagorean Theorem? The convere of a tatement witche the hypothei and the concluion. Statement: If p, then q. Convere of the tatement: If q, then p. 1 ACTIVITY: Analyzing Convere of Statement Work with a partner. Write the convere of the true tatement. Determine whether the convere i true or fale. If it i true, jutify your reaoning. If it i fale, give a counterexample. a. If a = b a = b 2 2, then. Convere: b. If a = b a = b 3 3, then. Convere: c. If one figure i a tranlation of another figure, then the figure are congruent. Convere: d. If two triangle are imilar, then the triangle have the ame angle meaure. Convere: I the convere of a true tatement alway true? alway fale? Explain. Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 161

22 Name Date 7.5 Uing the Pythagorean Theorem (continued) 2 ACTIVITY: The Convere of the Pythagorean Theorem Work with a partner. The convere of the Pythagorean Theorem tate: If the equation a + b = c i true for the ide length of a triangle, then the triangle i a right triangle. a. Do you think the convere of the Pythagorean Theorem i true or fale? How could you ue deductive reaoning to upport your anwer? b. Conider DEF with ide length a, b, and c, 2 2 uch that a + b = c 2. Alo conider JKL with leg length a and b, where K = 90. What doe the Pythagorean Theorem tell you about JKL? D a c E J b F What doe thi tell you about c and x? a x What doe thi tell you about DEF and JKL? K b L What doe thi tell you about E? What can you conclude? 162 Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

23 Name Date 7.5 Uing the Pythagorean Theorem (continued) 3 ACTIVITY: Developing the Ditance Formula Work with a partner. Follow the tep below to write a formula that you can ue to find the ditance between and two point in a coordinate plane. Step 1: Chooe two point in the coordinate plane that do not lie on the ame horizontal or vertical line. x, y and x, y. Label the point ( ) ( ) Step 2: Draw a line egment connecting the point. Thi will be the hypotenue of a right triangle y x Step 3: Draw horizontal and vertical line egment from the point to form the leg of the right triangle. Step 4: Ue the x-coordinate to write an expreion for the length of the horizontal leg Step 5: Ue the y-coordinate to write an expreion for the length of the vertical leg. Step 6: Subtitute the expreion for the length of the leg into the Pythagorean Theorem. Step 7: Solve the equation in Step 6 for the hypotenue c. What doe the length of the hypotenue tell you about the two point? What I Your Anwer? 4. IN YOUR OWN WORDS In what other way can you ue the Pythagorean Theorem? 5. What kind of real-life problem do you think the convere of the Pythagorean Theorem can help you olve? Copyright Big Idea Learning, LLC All right reerved. Big Idea Math Blue 163

24 Name Date 7.5 Practice For ue after Leon 7.5 Tell whether the triangle with the given ide length i a right triangle yd 10 yd 26 mm 18 yd 10 mm 24 mm 3. 4 m, 4.2 m, 5.8 m in., 35 in., 16 in. Find the ditance between the two point. 5. ( 2, 1 ), ( 3, 6) 6. ( 6, 4 ), ( 2, 2) 7. ( 1, 7 ), ( 4, 5) 8. ( 9, 3 ), ( 5, 8) 9. The cro-ection of a wheelchair ramp i hown. Doe the ramp form a right triangle? 25 in. 313 in. 312 in. 164 Big Idea Math Blue Copyright Big Idea Learning, LLC All right reerved.

Fair Game Review. Chapter 6 A B C D E Complete the number sentence with <, >, or =

Fair Game Review. Chapter 6 A B C D E Complete the number sentence with <, >, or = Name Date Chapter 6 Fair Game Review Complete the number entence with , or =. 1..4.45. 6.01 6.1..50.5 4. 0.84 0.91 Find three decimal that make the number entence true. 5. 5. 6..65 > 7..18 8. 0.0