Big Ideas Math Geometry 4.5 Answers

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Study Skills: Using The Features Of Your Textbook To Prepare For Quizzes And Tests

Mathematical Practices

Question 1.Provide a counter example for each false conditional statement in Exercises 17 24 on page 71.

Question 2.Create a truth table for each of your answers to Exercise 59 on page 74.Answer:

Question 3.For Exercise 32 on page 88. write a question you would ask your friend about his or her interpretation.Answer:

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Big Ideas Math Book Geometry Answer Key Chapter 4 Transformations

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Transformations

Tell whether the red figure is a translation, reflection, rotation, or dilation of the blue figure.

Question 1.Answer: The red figure is the mirror image of the blue figure so it is a reflection.

Question 2.Answer: The blue figure turns to form the red figure so it is a rotation.

Question 3.Answer: A dilation produces an image similar to the original figure. So, the blue polygon is a dilation of the red figure.

Question 4.Answer: The blue figure is similar to the red figure and one is a dilation of the other.

Tell whether the two figures are similar. Explain your reasoning.

Question 5.Length of A/Length of B = 12/14 = 6/7Width of A/Width of B = 5/7Thus Rectangle A and Rectangle B are not similar.

Question 6.Base of triangle A/Base of triangle B = 6/9 = 2/3Height of triangle A/Height of triangle B = 8/12 = 2/3Hypotenuse of triangle A/Hypotenuse of triangle B = 10/12 = 5/6Triangle A and Triangle B are similar.

Question 7.Length of A/Length of B = 6/3 = 2Width of A/Width of B = 10/5 = 2The two figures are similar.

Big Ideas Math Book Geometry Answer Key Chapter 2 Reasoning And Proofs

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Some rectangles are not squares.Therefore, some squares are not trapezoids.Answer:

If polygon ABCD is a square. then ills a rectangle.Polygon ABCD is a rectangle.Therefore, polygon ABCD is a square.Answer:

If polygon ABCD is a square, then it is a rectangle.Polygon ABCD is not a square.Therefore, polygon ABCD is not a rectangle.Answer:

Exploration 1

Determining Whether a Statement is True or False

Work with a partner: A hypothesis can either be true or false. The same is true of a conclusion. For a conditional statement to be true, the hypothesis and conclusion do not necessarily both have to be true. Determine whether each conditional statement is true or false. Justify your answer.

a. If yesterday was Wednesday, then today is Thursday.Answer:

b. If an angle is acute. then it has a measure of 30°.Answer:

c. If a month has 30 days. then it is June.Answer:

Exploration 2

Exploration 3

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Im An Algebra 2 Teacher And I Hate This App

Okay. I have a lot to say. 1. The app doesnt connect to homework2. No resources like website.3. The app only has the Spanish version available for my students 4. Not only do you have to download the app, you then have to download the book. 5. You cant search other textbooks to add to your library. Why? For a company that apparently wants to provide resources to students and make it accessible, why do you make it impossible. The vast majority of people have only cell phones, fewer have a tablet or laptop available also. I knew I disliked this book due to the order but man, you guys really sealed the deal by having a difficult system to use for student AND teachers alike. Way to be difficult guys.

Big Ideas Math Geometry Answers

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Exercise 46 Similarity And Transformations

Vocabulary and Core Concept Check

Question 1.What is the difference between similar figures and congruent figures?Answer:Congruent figures have the same size and shape. Similar figures have the same shape, but not necessarily the same size.

Question 2.A transformation that produces a similar figure. such as a dilation.is called a _________ .Answer: A transformation that produces a similar figure. such as a dilation is called a similarity transformation.

Monitoring Progress and Modeling with Mathematics

In Exercises 3-6, graph FGH with vertices F, G, and H and its image after the similarity transformation.

Question 3.Translation: Dilation: Answer:

Dilation: \\)Reflection: in the y-axisDilation: \\)F F’F’ FG’ GH’ H

Question 5.Rotation: 90° about the originDilation: Answer:

Dilation: \\)Reflection: in the x-axisFirst draw FGH with vertices F, G and HDilation: \\)Scale factor is \F = F’, \)G = G’, -3)H = H’F’, \) F, \)G’, -3) G, 3)H’ H

In Exercises 7 and 8. describe a similarity transformation that maps the blue preimage to the green image.

Question 7.

Answer:The similarity transformation that maps the blue preimage to green image is:Reflection on y-axis. Then dilation with the scale factor is 1/2 about the center point The length of \ = 4 unitsThe length of \ = 2 unitsScale factor =\ / \ = 2/4 = 1/2

Question 11.G, H, I and J, K, LAnswer:

In Exercises 13 and 14, prove that the figures are similar.

Maintaining Mathematical Proficiency

All About Common Core 2019 Curriculum

In a nutshell, Common Core is the kit of academic standards in English language Arts and Mathematics that represent what a student should figure out and learn by the end of each school year in elementary school Grade K to High School Grade 12th. Common Core Standards introduced in 2009 by the Council of Chief State School Officers and the National Governors Association Center for Best Practices . Both of these entities joined teams in a state-led effort to expand Common Core.

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Ncert Solutions For Class 8 Maths Chapter 4

The major concepts covered in the Chapter 4- Practical Geometry of include: 4.1 Introduction 4.2 Constructing a Quadrilateral 4.2.1 When the lengths of four sides and a diagonal are given 4.2.2 When two diagonals and three sides are given 4.2.3 When two adjacent sides and three angles are known 4.2.4 When three sides and two included angles are given 4.3 Some special cases

The Chapter 4 of NCERT Solutions for Class 8 Maths discusses the following:

Learning the chapter Practical Geometry enables the students to:

• Construction of Quadrilaterals:
• Given four sides and one diagonal
• Three sides and two diagonals
• Three sides and two included angles
• Two adjacent sides and three angles

Disclaimer:

Dropped Topics 4.1 Introduction, 4.2 Construction of quadrilateral and 4.3 Some special cases.

In A Rhombus Diagonals Bisect Each Other At 90 The Given Rhombus Abcd Can Be Drawn As Follows

Rough Figure:

Draw a line segment AC of 5.2 cm and draw its perpendicular bisector. Let it intersect the line segment AC at point O.

Draw arcs of 6.4/2 = 3.2 on both sides of this perpendicular bisector. Let the arcs intersect the perpendicular bisector at point B and D.

Join points B and D with points A and C.

ABCD is the required rhombus.

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Exercise 22 Inductive And Deductive Reasoning

Vocabulary and Core Concept Check

Question 1.How does the prefix counter help you understand the term counterexample?Answer:

In Exercises 9 12. make and test a conjecture about the given quantity.

Question 9.the product of any two even integersAnswer:

the sum of an even integer and an odd integerAnswer:

the quotient of a number and its reciprocalAnswer:

the quotient of two negative integersAnswer:

In Exercises 13 16, find a counter example to show that the conjecture is false.

Question 13.The product of two positive numbers is always greater than either number,Answer:

Question 14.If n is a nonzero integer, then \ is always greater than 1.Answer:

Question 15.If two angles are supplements of each other. then one of the angles must be acute.Answer:

Question 16.A line s divides \ into two line segments. So, the lines is a segment bisector of \Answer:

In Exercises 17 20. use the Law of Detachment to determine what you can conclude from the given information, if possible.

Question 17.If you pass the final, then you pass the class. You passed the final.Answer:

Question 18.If your parents let you borrow the ear, then you will go to the movies with your friend. you will go to the movies with your friend.Answer:

Question 19.If a quadrilateral is a square. then it has four right angles. Quadrilateral QRST has four right angles.Answer:

In Exercises 21 24, use the Law of Syllogism to write a new conditional statement that follows from the pair of true statements, if possible.

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Reasoning And Proofs Cumulative Assessment

Question 1.Use the diagram to write an example of each postulate.a. Two Point Postulate : Through any two points, there exists exactly one line.Answer:

b. Line Intersection Postulate : If two lines intersect, then their intersection is exactly one point.Answer:

c. Three Point Postulate : Through any three noncollinear points, there exists exactly one plane.Answer:

d. Plane-Line Postulate : If two points lie in a plane, then the line containing them lies in the plane.Answer:

e. Plane Intersection Postulate : If two planes intersect, then their intersection is a lineAnswer:

Enter the reasons in the correct positions to complete the two-column proof.Answer:

Classify each related conditional statement. based on the conditional statementIf I study, then I will pass the final exam.a. I will pass the final exam if and only if I study.Answer:

b. If I do not study, then I will not pass the final exam.Answer:

c. If I pass the final exam, then I studied.Answer:

d. If I do not pass the final exam, then I did not study.Answer:

List all segment bisectors given x = 3.Answer:

Question 5.You are given mFHE = mBHG = mAHF = 90°. Choose the symbol that makes each statement true. State which theorem or postulate. if any, supports your answer.

c. mFHE _______ mAHGAnswer:

d. mAHG + mGHE _______180°Answer:

Find the distance between each pair of points. Then order each linesegment from longest to shortest.a. A, BAnswer:

b. C, DAnswer:

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Ncert Solutions Class 8 Maths Chapter 4 Free Pdf Download

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry are useful for students as it helps them in scoring high marks in the examination. These NCERT Solutions contain detailed step-by-step explanations of all the problems that come under the Chapter 4 Practical Geometry of the Class 8 NCERT Textbook. By understanding the concepts used in NCERT Solutions for Class 8, students will be able to clear all their doubts related to Practical Geometry. These solutions are prepared by subject matter experts at BYJUS, describing the complete method of solving problems.

Lesson 23 Postulates And Diagrams

Monitoring progress

Question 1.Use the diagram in Example 2. Which postulate allows you to say that the intersection of plane P and plane Q is a line?Answer:

Use the diagram in Example 2 to write an example of the postulate.a. Two Point Postulate

H, F, and D are coplanar. Plane T plane S. Point B bisects \. ABH and HBF are a linear pair.

Question 24.HOW DO YOU SEE IT?Use the diagram of line m and point C. Make a conjecture about how many planes can be drawn so that line m and point C lie in the same plane. Use postulates too justify your conjecture.Answer:

Question 25.MATHEMATICAL CONNECTIONSOne way to graph a linear equation is to plot two points whose coordinates satisfy the equation and then connect them with a line. Which postulate guarantees this process works for any linear equation?Answer:

Question 26.MATHEMATICAL CONNECTIONSA way to solve a system of two linear equations that intersect is to graph the lines and find the coordinates of their intersection. Which postulate guarantees this process works for an two linear equations?Answer:

In Exercises 27 and 28, rewrite the postulate in if-then form. Then write the converse, inverse, and contrapositive and state which ones are true.

Question 27.Two Point Postulate Answer:

Question 31.MAKING AN ARGUMENTYour friend claims that even though two planes intersect in a line, it is possible for three planes to intersect in a point. Is your friend correct? Explain your reasoning.Answer:

Question 35.

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