Geometry 1.1 1.3 Answers

Measuring And Constructing Angles

1.1 Introduction to Geometry

Essential Question

How can you measure and classify an angle?Answer:An angle is formed when two rays have the same endpoint or vertex.An Angle will be measured by using a protractorClassification of angles:An angle can be classified according to the size of theopening between its rays.An acute angle measures greater than 0° and lessthan 90°.A right-angle forms a square corner and measures 90°.An obtuse angle measures greater than 90° and less than 180°

Exploration 1

Measuring and Classifying Angles

Work with a partner: Find the degree measure of each of the following angles. Classify each angle as acute, right, or obtuse.a. AOB

a. Use a ruler and protractor to draw the triangular pattern shown at the right.Answer:The representation of the triangular pattern by using a ruler and a protractor is:

b. Cut out the pattern and use it to draw three regular hexagons

C. The sum of the angle measures of a polygon with n sides is equal to 180°. Do the angle measures at your hexagons agree with this rule? Explain.ATTENDING TO PRECISIONTo be proficient in math, you need to calculate and measure accurately and efficiently.Answer:It is given that the sum of the angle measures of a polygon with n sides is equal to 180 °This rule will be applicable for all the angle measures of all polygonsHence,We can conclude that the above rule will be applicable for the angle measures of the hexagon

Using Midpoint And Distance Formulas

EssentiaI QuestionHow can you find the midpoint and length of a line segment in a coordinate plane?Answer:Let the line segment is formed by the points A , B So,The coordinates of the midpoint of the line segment are given as:M = , \)The length of the line segment in a coordinate plane is given as:D = \

Exploration 1

Finding the Midpoint of a Line Segment

Work with a partner.

a. Graph \, where the points A and B are as shown.Answer:We can conclude that the length of \ is: 10cmThe representation of \ is:

b. Explain how to bisect \, that is, to divide AB into two congruent line segments. Thenbisects \ and use the result to find the midpoint M of \.Answer:The steps to find the bisector of \ is:a. Place the compass at one end of the line segmentb. Adjust the compass to slightly longer than half of the line segment lengthc. Draw arcs above and below the lined. Keeping the same compass width, draw arcs from the other end of linee. Place ruler where the arcs cross and draw the line segmentNow,The representation of \ is:Now,The representation of the perpendicular bisector and the midpoint M of \ is:Hence, from the above figure,The midpoint of \ is: 5 cm

c. What are the coordinates of the midpoint M?Answer:The coordinates of the midpoint of the line segment are given as:M = , \)So,M = ,\)M = ,\)M = Hence,The coordinates of the midpoint M is:

Exploration 2

d. Use the Pythagorean Theorem and point M from Exploration 1 to find the lengths of \ and \. What can you conclude?Answer:

Measuring And Constructing Segments

Essential QuestionHow can you measure and construct a line segment?Answer:The steps used to measure a line segment are:a. Pick up a scale to measure the length of a line segment.b. Identify the line segment you want to measurec. Place the tip of the ruler at the starting of the line segment

The steps used to construct a line segment are:a. Place the compass at one end of the lineb. Adjust the compass to slightly longer than half of the lines lengthc. Draw arcs above and below the lined. Keeping the same compass width, draw arcs from the other end of the linee. Place ruler where the arcs cross and draw the line segment

Exploration 1

Measuring Line Segments Using Nonstandard Units

Work with a partner.

a. Draw a line segment that has a length of 6 inches.Answer:We will use a ruler to draw a line segment and the ruler we use generally is the Centimeter rulerBut,It is given that we have to draw a line segment that has a length of 6 inchesBut, it is not possibleSo,6 inches = 15.24 cmHence,The representation of the line segment that has the length of 6 inches in terms of cm is:

c. Write conversion factors from paper clips to inches and vice versa.Answer:We can conclude that the conversion of paper clips into inches and vice-versa is:1 paperclip = 1.377 inch1 inch = 2.54 paperclip

Exploration 2

Measuring Line Segments Using Nonstandard Units

Work with a partner.

Exploration 3

Measuring Heights Using Nonstandard Units

Work with a partner.

Communicate Your Answer:

Big Ideas Math Book Geometry Answer Key Chapter 1 Basics Of Geometry

You can avail the Big Ideas Math Geometry Answer Key Ch 1 during your preparation aligned as per the Big Ideas Math Geometry Textbooks. Clarify all your concerns taking the help of the Big Ideas Math Geometry Chapter 1 Answer Key and clear the exam with flying colors. For a better searching experience, we have curated the Topicwise BIM Book Geometry Answer Key through the quick links. Just tap on them and ace up your preparation recording to subject requirements.

We can conclude that the area of the given triangle is: 200 in²

Question 13.ABSTRACT REASONINGDescribe the possible values for x and y when |x y| > 0. What does it mean when |x y| = 0 ? Can |x y| < 0? Explain your reasoning.Answer:We know that,The value of the absolute expression must be greater than or equal to 0 but not less than 0So,The values for | x y | do not existNow,The possible values of | x y | > 0 should be greater than 0 and maybe x > y and x < yThe possible values of | x y | = 0 should be only one value i.e., 0 as x and y must be equal to make the difference value 0

Balbharati Solutions For Mathematics 2 Geometry 9th Standard Maharashtra State Board Chapter 1 Basic Concepts In Geometry Problem Set 1

Select the correct alternative from the answer of the question given below.

How many mid points does a segment have?

only one

Select the correct alternative from the answer of the question given below.

infinite

Select the correct alternative from the answer of the question given below.

On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.

d + d = d

On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.

d + d = d

On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statements are true or false.

d + d = d

On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statements are true or false.

d – d = d

Co-ordinates of the pair of a point is given below. Hence find the distance between the pair.

3, 6

Co-ordinates of the pair of points are given below. Hence find the distance between the pair.

-9, -1

Co-ordinates of the pair of points are given below. Hence find the distance between the pair.

-4, 5

x, -2

x + 3, x – 3

-25, -47

80, – 85

Answer the following question.

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Balbharati Solutions For Mathematics 2 Geometry 9th Standard Maharashtra State Board Chapter 1 Basic Concepts In Geometry Practice Set 12

The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not.

Point

seg DE and seg AB

seg BC and seg AD

seg BE and seg AD

Point M is the midpoint of seg AB. If AB = 8 then find the length of AM.

Point P is the midpoint of seg CD. If CP = 2.5, find l.

If AB = 5 cm, BP = 2 cm and AP = 3.4 cm, compare the segments.

Write the answers to the following questions with reference in the given figure.

Answer the questions with the help of a given figure.

Basics Of Geometry Mathematical Practices

Monitoring Progress

Question 1.Find the area of the polygon using the specified units. Round your answer to the nearest hundredth.Answer:

The differences between a line, a ray, and a line segment are:A Ray has no starting and ending pointsA line has a starting point but no ending pointA line segment has both starting point and an ending point

Exploration 2

Intersections of Lines and Planes

Work with a partner:a. Describe and sketch the ways in which two lines can intersect or not intersect. Give examples of each using the lines formed by the walls. floor. and ceiling in your classroom.Answer:Examples of non-intersecting lines are: Floor and ceilingExamples of intersecting lines are: Walls and floor

b. Describe and sketch the ways in which a line and a plane can intersect or not intersect. Give examples of each using the walls. floor, and ceiling in your classroom.Answer:Examples of the intersection of a plane and a line are: Walls and ceilingExamples of the non-intersection of a plane and a line are: Floor and a blackboard

c. Describe and sketch the ways in which two planes can intersect or not intersect. Give examples of each using the walls. floor, and ceiling in your classroom.Answer:Examples of the intersection of planes are: Floor and benchesExamples of the non-intersection of planes are: Floor and ceiling

Exploration 3

Exploring Dynamic Geometry Software

Communicate Your Answer

Read Also: Define Variability In Math

Performance Task: Comfortable Horse Stalls

Mathematical Practices

Question 1.How could you explain your answers to Exercise 33 on page 36 to a friend who is unable to hear?Answer:In Exercise 33 on page 36,The given vertices of the triangle are in the form of the standard linear equationSo,Compare the given vertices with the standard linear equation and find the slopes and x and y-intercepts for the coordinates of the vertices of the triangle

Question 2.What tool could you use to verify your answers to Exercises 25 30 on page 44?Answer:To verify the answers to Exercise 25 30 on page 44,We can use Angle Addition Postulate

Question 3.Your friend says that the angles in Exercise 28 on page 53 are supplementary angles. Explain why you agree or disagree.Answer:In Exercise 28 on page 53,It is given that a right-angled triangle is formedWe know that,The sum of the complementary angles is: 90°Hence, from the above,We can conclude that you disagree with your friend about supplementary angle

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1 1 = 3 Proof | Breaking the rules of mathematics

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Study Skills: Keeping Your Mind Focused

1.1 1.3 What did you learn

Mathematical Practices

Question 1.Sketch an example of the situation described in Exercise 49 on page 10. Label your figure.Answer:The representation of the example of the situation described in Exercise 49 on page 10 is:

Question 2.Explain how you arrived at your answer for Exercise 35 on page 18.Answer:we arrived at the answer for Exercise 35 on page 18 by using the distance formula between 2 points.We know that,The distance between the 2 points = \

Question 3.What assumptions did you make when solving Exercise 43 0n page 26?Answer:The assumptions we make when solving Exercise 43 on page 26 is:All the lengths between the 2 points in the segment are equal

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Basics Of Geometry Chapter Review

1.1 Points, Lines, and Planes

Use the diagram.

Give another name for plane M.Answer:

We can conclude that the value of XZ is: 11

Question 9.Plot A, B, C, and D in a coordinate plane.Then determine whether \ and \ are congruent.Answer:A , B , C , and D Compare the given points withA , B , C , and D Now,\ = \= \= 5\ = \= \= 4The representation of the given points in the coordinate plane is:\ is not congruent to \

1.3 Using Midpoint and Distance Formulas

Find the coordinates of the midpoint M. Then find the distance between points S and T.

Question 10.S and TAnswer:S and T We know that,The coordinates of the Midpoint = , \)So,The coordinates of the Midpoint = , \)The coordinates of the Midpoint = , \ )Hence, from the above,We can conclude that the coordinates of the Midpoint are: , \)

Question 11.S and TAnswer:S and T We know that,The coordinates of the Midpoint = , \)So,The coordinates of the Midpoint = , \)The coordinates of the Midpoint = , \)Hence, from the above,We can conclude that the coordinates of the Midpoint are: , \)

Question 12.The midpoint of \ is M. One endpoint is J. Find the coordinates of endpoint K.Answer:The given points of \ are:M and J Let H be We know that,The coordinates of the Midpoint = , \)So, = , \)\ = 6 \ = 3x + 14 = 6 y + 9 = 3 x = 12 14 y = 6 9x = -2 y = -3We can conclude that the coordinates of H are:

1.4 Perimeter and Area in the Coordinate Plane

Find the perimeter and area of the polygon with the given vertices.

Question 7.