lesson 3 homework practice dilations answer key

Geo.3 Similarity

In this unit, students use dilations and rigid transformations to justify triangle similarity theorems including the Angle-Angle Triangle Similarity Theorem. Students explicitly build on their work with congruence and rigid motions, establishing that triangles are similar by dilating them strategically. The unit balances a focus on proof with a focus on using similar triangles to find unknown side lengths and angle measurements.

Properties of Dilations

• 1 Scale Drawings
• 2 Scale of the Solar System
• 3 Measuring Dilations
• 4 Dilating Lines and Angles
• 5 Splitting Triangle Sides with Dilation, Part 1

Similarity Transformations and Proportional Reasoning

• 6 Connecting Similarity and Transformations
• 7 Reasoning about Similarity with Transformations
• 8 Are They All Similar?
• 9 Conditions for Triangle Similarity
• 10 Other Conditions for Triangle Similarity
• 11 Splitting Triangle Sides with Dilation, Part 2
• 12 Practice With Proportional Relationships

Similarity in Right Triangles

• 13 Using the Pythagorean Theorem and Similarity
• 14 Proving the Pythagorean Theorem
• 15 Finding All the Unknown Values in Triangles

Putting It All Together

• 16 Bank Shot

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High school geometry

Course: high school geometry   >   unit 1.

• Dilating points
• Dilate points
• Dilations: scale factor
• Dilations: center
• Dilating shapes: expanding
• Dilating shapes: shrinking
• Dilating triangles: find the error

Dilate triangles

• Performing transformations FAQ
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• (Choice B)   B
• (Choice C)   C
• (Choice D)   D

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Texas Math Course 3, Grade: 8 Publisher: Glencoe/McGraw-Hill

Texas math course 3, title : texas math course 3, publisher : glencoe/mcgraw-hill, isbn : not available, isbn-13 : 9780076657087, use the table below to find videos, mobile apps, worksheets and lessons that supplement texas math course 3., textbook resources.

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Eureka Math Grade 8 Module 3 Lesson 3 Answer Key

Engage ny eureka math 8th grade module 3 lesson 3 answer key, eureka math grade 8 module 3 lesson 3 example answer key.

Eureka Math Grade 8 Module 3 Lesson 3 Exercise Answer Key

Exercises 1–2.

Exercise 2. What shape was the dilated image? Answer: The dilated image was an ellipse. Dilations map ellipses to ellipses.

Eureka Math Grade 8 Module 3 Lesson 3 Problem Set Answer Key

Students practice dilating a curved figure and stating the scale factor that would bring a dilated figure back to its original size.

Question 2. Describe the process for selecting points when dilating a curved figure. Answer: When dilating a curved figure, you have to make sure to use a lot of points to produce a decent image of the original figure. You also have to make sure that the points you choose are not all concentrated in just one part of the figure.

Question 3. A figure was dilated from center O by a scale factor of r=5. What scale factor would shrink the dilated figure back to the original size? Answer: A scale factor of r=\(\frac{1}{5}\) would bring the dilated figure back to its original size.

Question 4. A figure has been dilated from center O by a scale factor of r=\(\frac{7}{6}\). What scale factor would shrink the dilated figure back to the original size? A scale factor of r=\(\frac{6}{7}\) would bring the dilated figure back to its original size.

Question 5. A figure has been dilated from center O by a scale factor of r=\(\frac{3}{10}\). What scale factor would magnify the dilated figure back to the original size? Answer: A scale factor of r=\(\frac{10}{3}\) would bring the dilated figure back to its original size.

Eureka Math Grade 8 Module 3 Lesson 3 Exit Ticket Answer Key

Question 2. What scale factor would magnify the dilated circle back to the original size of circle A? How do you know? Answer: A scale factor of r=2 would bring the dilated circle back to the size of circle A. Since the circle was dilated by a scale factor of r=\(\frac{1}{2}\), then to bring it back to its original size, you must dilate by a scale factor that is the reciprocal of \(\frac{1}{2}\), which is 2.

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Texas Go Math Grade 8 Lesson 13.3 Answer Key Dilations and Measurement

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 13.3 Answer Key Dilations and Measurement.

Texas Go Math Grade 8 Lesson 13.3 Explore Activity Answer Key

Exploring Dilations and Measurement

What scale factor was used to dilate the green rectangle to the blue rectangle? Answer: The scale factor is used to dilate the green rectangle to the blue rectangle. Scalar factor = A’B’/AB = 8/4 = 4cm Scalar factor = B’C’/BC = 6/3 = 3cm Scalar factor = C’D’/CD = 8/4 = 4cm Scalar factor = D’A’/DA = 6/3 = 3cm

How are the side lengths of the blue rectangle related to the side lengths of the green rectangle? The sides of the blue rectangle are double times the green rectangle. The lengths of the green rectangle. The length of AB = 4cm The length of BC = 3cm The length of CD = 4cm The length of DA = 3cm The lengths of the blue rectangle. The length of AB’ = 8cm The length of B’C’ = 6cm The length of C’D’ = 8cm The length of D’A’ = 8cm

B. What is the perimeter of the green rectangle? _______________ What is the perimeter of the blue rectangle? _______________ How is the perimeter of the blue rectangle related to the perimeter of the green rectangle? Answer: i. The formula for the perimeter of the rectangle = 2(l + w) The length of the green rectangle = 4cm The width of the green rectangle = 3cm. P = 2(4 + 3) P = 14 The perimeter of the green rectangle = 14cm ii. The formula for the perimeter of the rectangle = 2(l + w) The length of the blue rectangle = 8cm The width of the blue rectangle = 6cm. P = 2(8 + 6) P = 28 The perimeter of the blue rectangle = 28cm iii. The perimeter of the green rectangle = 14cm The perimeter of the blue rectangle = 28cm The perimeter of the green rectangle is half of the blue rectangle.

C. What is the area of the green rectangle? _______________ What is the area of the blue rectangle? _______________ How is the area of the blue rectangle related to the area of the green rectangle? Answer: i. The formula for the area of the rectangle = l x w The length of the green rectangle = 4cm The width of the green rectangle = 3cm. A = 4 x 3 A = 12 The area of the green rectangle = 12 square units. ii. The formula for the perimeter of the rectangle = l x w The length of the blue rectangle = 8cm The width of the blue rectangle = 6cm. P = 8 x 6 P = 48 iii. The area of the green rectangle = 12 square units The area of the blue rectangle = 48 square units. The area of the green rectangle is 4 times the blue rectangle.

Question 2. Johnson Middle School is selling mouse pads that are replicas of a student’s award-winning artwork. The rectangular mouse pads are dilated from the original artwork and have a length of 9 inches and a width of 8 inches. The perimeter of the original artwork is 136 inches. What is the area of the original artwork? Answer: Given that, The perimeter of the original artwork = 136inches. The formula for the perimeter of the rectangle = 2(l +b) The length of the dilated mouse = 9inches The Width of the dilated mouse = 8 inches. The length of the original mouse = 9 x 4 = 36inches. The width of the original mouse = 8 x 4 = 32 inches. = 2(36 + 32) = 136 inches. Area of the rectangle = l x b = 36 x 32 = 1152inches. The area of the original artwork = 1152 inches.

Texas Go Math Grade 8 Lesson 13.3 Guided Practice Answer Key

Find the perimeter and area of the image after dilating the figures shown with the given scale factor. (Explore Activity and Example 1)

A group of friends is roping off a soccer field in a back yard. A full-size soccer field is a rectangle with a length of 100 yards and a width of 60 yards. To fit the field in the back yard, the group needs to reduce the size of the field so its perimeter is 128 yards. (Example 1)

Question 3. What is the perimeter of the full-size soccer field? Answer: The length of the soccer field = 100 yards. The width of the soccer field = 60 yards. The perimeter of the rectangle = 2(l + b) = 2(100 + 60) = 320yards The perimeter of the full-size soccer field = 320 yards.

Question 4. What is the scale factor of the dilation? Answer: The dilation soccer field perimeter = 128 yards. The formula for the perimeter of the rectangle = 2(l + b) The length of the soccer field = 100 yards. The width of the soccer field = 60 yards The length of the dilated field = 42 yards. The length of the dilated field is 2.4 times less than the original length. The width of the dilated field = 22 yards The width of the dilated field is 2.7 times less than the original width. Scale factor of the dilation = larger length/smaller length = 100/42 = 2.38 The scale factor of the dilation = 21/50

Question 5. What is the area of the soccer field in the backyard? Answer: The formula for the area of the rectangular soccer field in the backyard = l x b The length of the soccer field in the backyard = 100 yards. The width of the soccer field in the backyard = 60 yards. = 100 x 60 = 6000 square yards. The area of the rectangular soccer field in the backyard = 6000 square yards.

Essential Question Check-In

Lesson 13.3 Dilations and Measurement Answers 8th Grade Question 6. When a rectangle is dilated, how do the perimeter and area of the rectangle change? Answer: The perimeter of the dilated rectangular soccer field in the backyard = 128 yards. The perimeter of the original rectangular soccer field in the backyard = 2(100 + 60) = 130 yards The area of the rectangular soccer field in the backyard = 6000 square yards. The area of the dilated rectangle = 42 x 22 = 924. The perimeter and area of the rectangle are less than the original rectangle.

Texas Go Math Grade 8 Lesson 13.3 Independent Practice Answer Key

Question 7. When you make a photocopy of an image, is the photocopy a dilation? What is the scale factor? How do the perimeter and area change? Answer: Assume that the image is in the shape of a rectangle. Dilation length = 4cm Dilation Breadth = 2cm Perimeter of the dilation photocopy = 2(4 + 2) = 12 The area of the dilation photocopy = l x b = 4 x 2 = 8 square cm Scale factor 4/2 = 2.

Question 8. Problem-Solving The universally accepted film size for movies has a width of 35 millimeters. If you want to project a movie onto a square sheet that has an area of 100 square meters, what is the scale factor that is needed for the projection of the movie? Explain. Answer: The film size for movies has a width = 35 millimeters. The movie onto a square sheet that has an area = 100 square meters. Width od the square sheet = 4a = 100/4 = 25mm Scale factor = 35/25 = 7/5.

Question 9. The perimeter of a square is 48 centimeters. If the square is dilated by a scale factor of 0.75, what is the length of each side of the new square? Answer: Given that, The perimeter of a square = 48 centimeters 48/4 = 12. The formula for the perimeter of the square = 4a The square is dilated by a scale factor = 0.75, The length of each side of a square = 12. The length of the new square = 12 x 0.75 = 9 cm.

Lesson 13.3 Grading Scale Texas Go Math 8th Grade Question 10. The screen of an eReader has a length of 8 inches and a width of 6 inches. Can the page content from an atlas that measures 19 inches by 12 inches be replicated in the eReader? If not, propose a solution to move the atlas content into the eReader format. Answer: The screen of an eReader length = 8 inches. The screen of an eReader width of 6 inches. The page content from an atlas that length = 19 inches. The page content from an atlas that breadth = 12 inches The page content of the atlas cannot be replicated on the eReader.

Question 11. Represent Real-World Problems There are 64 squares on a chessboard. Each square on a tournament chessboard measures 2.25 × 2.25 inches. A travel chessboard is a dilated replica of the tournament chessboard using a scale factor of \(\frac{1}{3}\).

a. What is the size of each square on the travel chessboard? Answer: The size of each square on the travel chessboard is 2.25 x 2.25 = 5.062.

b. How long is each side of the travel board? Answer: Each side of the travel board = 2.25 inches.

c. How much table space do you need to play on the travel chessboard? Answer: The number of squares on the chessboard = 64. The size of each square = 5.062. The tablespace on the travel chessboard = 64 x 5.062 = 323.968.

Question 12. Draw Conclusions The legs of a right triangle are 3 units and 4 units long. Another right triangle is dilated from this triangle using a scale factor of 3. What are the side lengths and the perimeter of the dilated triangle? Answer: The legs of a right rectangle = 3 units and 4 units. Scale factor = 3. The side lengths of the dilated triangle = 3 x 3 = 9 And 4 x 3 = 12 The side lengths of the dilated triangle = 9 units and 12 units Perimeter of the dilated triangle = P = a + b + √(a²+ b²) A = 9units B = 12 units P = 9 + 12 + √(9²+ 12²) = 9 + 12 + 153 The perimeter of the dilated triangle = 174 units.

H.O.T. Focus on Higher Order Thinking

Texas Grading Scale Go Math Grade 8 Question 14. Multistep Rectangle A’B’C’D’ is a dilation of rectangle ABCD, and the scale factor is 2. The perimeter of ABCD is 18 mm. The area of ABCD is 20 mm 2 . a. Write an equation for, and calculate, the perimeter of A’B’C’D’. Answer: The perimeter of ABCD is 18 mm. Rectangle A’B’C’D’ is a scale factor of 2. The perimeter of A’B’C’D’ = 18 x 2 = 32mm

b. Write an equation for, and calculate, the area of A’B’C’D’. Answer: The area of ABCD is 20 mm². The area of the A’B’C’D’ = ABCD area x square of scale factor. = 20 x 2² = 80mm²

c. The side lengths of both rectangles are whole numbers of millimeters. What are the side lengths of ABCD and A’B’C’D’? Answer: The perimeter of ABCD is 18 mm. The formula for the perimeter of the rectangle = 2(l + b). Scale factor = 2 The sides lengths of the ABCD = 18/2 = 9mm The perimeter of A’B’C’D’ = 18 x 2 = 32mm The sides lengths of the A’B’C’D’ = 32/2 = 16mm

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Chapter 6 Lesson 4 Skills Practice Dilations Answer Key

Chapter 6 Lesson 4 Skills Practice Dilations Answer Key - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are 01 h find the vertices of each figure after a dilation, Name date period lesson 4 skills practice, Lesson 4 reteach, Name date period lesson 1 skills practice, Name date period lesson 4 skills practice, Chapter 4 resource masters, Practice your skills with answers, Scale drawings and scale factor.

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1. (01 H ) Find the vertices of each figure after a dilation ...

2. name date period lesson 4 skills practice, 3. lesson 4 reteach -, 4. name date period lesson 1 skills practice, 5. name date period lesson 4 skills practice, 6. chapter 4 resource masters, 7. practice your skills with answers, 8. scale drawings and scale factor.

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