Measuring And Constructing Angles
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 rightangle 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 viceversa 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:
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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.
Select the correct alternative from the answer of the question given below.
Select the correct alternative from the answer of the question given below.
On a number line, coordinates 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, coordinates 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, coordinates 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, coordinates of P, Q, R are 3, 5 and 6 respectively. State with reason whether the following statements are true or false.
d – d = d
Coordinates of the pair of a point is given below. Hence find the distance between the pair.
3, 6
Coordinates of the pair of points are given below. Hence find the distance between the pair.
9, 1
Coordinates 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 coordinates. 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 nonintersecting 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 nonintersection 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 nonintersection of planes are: Floor and ceiling
Exploration 3
Exploring Dynamic Geometry Software
Communicate Your Answer
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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 yintercepts 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 rightangled 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
Faqs On High School Bim Textbook Geometry Answers
1. Is there any reliable source that provides Big Ideas Math Geometry Answers for all Chapters?
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2. Where do I find Free Easy Access Student Edition of Big Ideas Math Geometry Answer Key?
You can find the Free Easy Access Student Edition of Big Ideas Math Geometry Answer Key on our page.
3. How to download High School BigIdeas Math Geometry Solutions PDF?
All you have to do is simply click on the quick links available for Geometry Big Ideas Math Answers to download them.
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Why To Read Geometry Bigideas Math Answer Key
You can have numerous benefits of referring to the Geometry Big Ideas Math Answers and they are listed in the below sections.
 Geometry Big Ideas Math Textbook Solutions are prepared by subject experts keeping in mind the Common Core Curriculum 2019.
 You can answer any kind of question from Performance Test, Chapter Test, Practice Test, Cumulative Practice if you solve the BIM Geometry Answer Key regularly.
 Big Ideas Math Book Answers for Geometry educates the High School Kids to become proficient in Geometry Concepts.
 Make the most out of this quick guide and become a master in the subject and inculcate problemsolving skills.
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.
Balbharati Solutions For Mathematics 2 Geometry 9th Standard Maharashtra State Board Chapter 1 Basic Concepts In Geometry Practice Set 11
Find the distances with the help of the number line given below.
If the coordinate of A is x and that of B is y, find d.
x = 1, y = 7
If the coordinate of A is x and that of B is y, find d.
x = 6, y = – 2
If the coordinate of A is x and that of B is y, find d.
x = – 3, y = 7
If the coordinate of A is x and that of B is y, find d.
x = – 4, y = – 5
If the coordinate of A is x and that of B is y, find d.
x = – 3, y = – 6
If the coordinate of A is x and that of B is y, find d.
x = 4, y = – 8
From the information given below, find which of the point is between the other two. If the points are not collinear, state so.
d = 7, d = 10, d = 3
From the information given below, find which of the point is between the other two.If the points are not collinear, state so.
d = 8, d = 6, d = 4
From the information given below, find which of the point is between the other two.If the points are not collinear, state so.
d = 16, d = 9, d = 7
From the information given below, find which of the point is between the other two.If the points are not collinear, state so.
d = 11, d = 12, d = 8
From the information given below, find which of the point is between the other two.If the points are not collinear, state so.
d = 15, d = 7, d = 8
From the information given below, find which of the point is between the other two.If the points are not collinear, state so.
d = 5, d = 8, d = 6
Which figure is formed by three noncollinear points?
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Describing Pairs Of Angles
Essential Question
How can you describe angle pair relationships and use these descriptions to find angle measures?Answer:Two adjacent angles are a linear pair when their noncommon sides are opposite rays. The angles in a linear pair are supplementary angles. common side L1+22=180°. Two angles are vertical angles when their sides form two pairs of opposite rays
Exploration 1
Work with a partner: The fivepointed star has a regular pentagon at its center.
a. What do you notice about the following angle pairs?x° and y°
We can observe that c and e are the opposite anglesSo,We can say that,c° = e°
b. Find the values of the indicated variables. Do not use a protractor to measure the angles.Explain how you obtained each answer.Answer:The given figure is: SquareSo,All the angles in the square are: 90°Hence, from the above,c° = 90°, d° = 90°, and e° = 90°
Communicate Your Answer
How can you describe angle pair relationships and use these descriptions to find angle measures?Answer:Two adjacent angles are a linear pair when their noncommon sides are opposite rays. The angles in a linear pair are supplementary angles. common side L1+22=180°. Two angles are vertical angles when their sides form two pairs of opposite rays