## 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

## Big Ideas Math Geometry Answers Chapter 1 Basics Of Geometry

Looking across the web for a friendly site that caters to all your needs regarding the Big Ideas Math Geometry Concepts? Dont worry we are with you in this and we will provide you the Complete Big Ideas Math Geometry Answers Chapter 1 Basics of Geometry. All the Solutions covered in the BIM Geometry Ch 1 Basics of Geometry Answer Key are as per the latest Common Core State Standards guidelines. Practice using the BigIdeas Math Chapter 1 Solutions via quick links available and clear the exams with flying colors.

## Lesson 16 Describing Pairs Of Angles

**Monitoring Progress**

In Exercises 1 and 2. use the figure.

Question 1.Name a pair of complementary angles, a pair of supplementary angles, and a pair of adjacent angles.Answer:We know that,The pair of angles that the sum of the angle measures is 90° is called Complementary anglesThe pair of angles that the sum of the angle measures is 180° is called Supplementary anglesThe angle that is the same in more than 1 angle-pair is called Adjacent AngleSo,The pair of complementary angles is: FGK and LKGThe pair of supplementary angles is: HGK and GKLThe pair of adjacent angles is: FGK and HGK

Question 2.Are KGH and LKG adjacent angles? Are FGK and FGH adjacent angles? Explain.Answer:The angle that is the same in more than 1 angle-pair is called Adjacent AngleBut,In KGH and LKG, the angle is not the sameSo,KGH and LKG are not the adjacent anglesIn FGK and FGH, the angle is the sameSo,FGK and FGH are adjacent angles

Question 3.1 is a complement of 2. arid m2 = 5°. Find m1.Answer:We know that,The pair of angles that the sum of the angle measures is 90° is called Complementary anglesIt is given that1 is a complement of 2So,It is also given that2 = 5°

LMN = 26° and PQR = 64°

**Also Check: Holt Geometry Workbook Answers **

## Lesson 11 Points Lines And Planes

**Monitoring Progress**

Use the diagram in Example 1. Give two other names for . Name a point that is not coplanar with points Q. S, and T.Answer:The definition of a ray is:A ray has no starting and ending pointsSo,The other names for \ are: Line m and \We know that,Co-planar points are the points if all of them lie in the same planeHence, among the points Q, S, and T,S and T are co-planar since they lie in the same plane and Q is not co-planar

Question 2.Give another name for \.Answer:

\P and \K are not the same rayReason:\ is the ray and KP is the line segmentNow,We can also observe that\P and \M are in the same rayReason:Since the points N, P, and M are collinear, the ray \M and \P are in the same plane

Question 4.Sketch two different lines that intersect a plane at the same point.Answer:The representation of the two different lines that intersect a plane at the same point is:

Question 5.

The points that are present in the same plane are called Co-planar pointsHence, from the above,We can conclude that the point that is co-planar with R, S, and T is: W

In Exercises 11 16, use the diagram.

Question 11.What is another name for \?Answer:

Question 13.What is another name for ray \E?Answer:

Name all rays with endpoint E.Answer:Hence, from the above figure,We can conclude that the rays with endpoint E are: s and t

Question 15.Name two pairs of opposite rays.Answer:

In Exercises 17 24, sketch the figure described.

Question 19.

Question 25.

Question 35.

Question 51.

## Exercise 15 Measuring And Constructing Angles

Vocabulary and Core Concept Check

Question 1.Two angles are __________ angles when they have the same measure.Answer:

**WHICH ONE DOES DOESNT BELONG?**Which angle name does not belong with the other three? Explain your reasoning.BCA

The steps to copy the angle are:Step 1:Label the vertex of the original angle as A. Draw a segment and label a point D on the segment.Step 2:Draw an arc with the center at A. Label the two intersecting points as B and C.Step 3:Using the same radius, draw an arc with center D. Label the intersecting point as E.Step 4:Draw an arc with radius BC and center E. Label the intersection F.Step 5:

In Exercises 17 20, in mAED = 34° and mEAD = 112°.

Question 17.Identify the angles congruent to IED.Answer:

Identify the angles congruent to EAD.Answer:The angles congruent to EAD are:DBC, ADB, and DAE

The steps for the construction of the angle bisector and copying of the angle is:Step 1:Label the vertex of the angle as A. Place the compass at A.Step 2:Draw an arc that intersects both sides of the angle. Label the intersections B and C.Step 3:Place the compass at C and draw an arc, then place the compass point at B. Using the same radius, draw another arc. Label the intersection D.Step 4:Use a straightedge to draw a ray through A and D.Step 5:\ bisects A

In Exercises 33 36, \S bisects PQR. Use the diagram and the given angle measure to find the indicated angle measures.

Question 33.mPQS = 63°. Find mRQS and mPQR.Answer:

= 56°

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## Exercise 14 Perimeter And Area In The Coordinate Plane

Question 1.The perimeter of a square with side length s is P = _________ .Answer:

Question 2.**WRITING**What formulas can you use to find the area of a triangle in a coordinate plane?Answer:We know that,The formula you can use to find the area of a triangle in a coordinate plane is:Area of a triangle = \ × Base × Height

Monitoring Progress and Modeling with Mathematics

In Exercises 3 6, classify the polygon by the number of sides. Tell whether it is convex or concave.

Question 3.

The number of sides is: 6We know that,The figure is concave if all the interior angles are greater than 180°The figure is convex if all the interior angles are less than 180°Hence, from the above,We can conclude that the given polygon is a hexagon and it is a concave polygon as it has interior angles greater than 180°

In Exercises 7 12. find the perimeter of the polygon with the given vertices.

Question 7.G, H, J, KAnswer:

Q, R, s, TAnswer:The given vertices of a polygon are:Q , R , S , T Now,The length of QR = \=\= 4The length of RS = \=\= 4The length of ST = \=\= 4The length of TQ = \= \= 4From the lengths of all of the sides,We can say that the vertices belong to a squareSo,The perimeter of a square = 4 × Side= 4 × 4We can conclude that the perimeter of the given polygon is: 16

Question 9.U, V, WAnswer:

Question 11.

In Exercises 13 16. find the area of the polygon with the given vertices.

Question 13.E, F, GAnswer:

Question 15.W, X, Y, ZAnswer:

In Exercises 17 24, use the diagram.

## Lesson 13 Using Midpoint And Distance Formulas

**Monitoring Progress**

Identify the segment, bisector of \. Then find PQ.

Question 1.The given line segment is:We know that,A segment has a starting point and an ending pointSo,The bisector of \ is: MNNow,From the above figure,The bisector divided the given line segment into 2 equal parts and given the length of 1 partSo,\ = 1\Hence,The length of \ = \ + \= 2 × 1\= 2 × \= \ × \= \We can conclude that the length of \ is: \

Question 2.The given line segment is:We know that,A segment has a starting point and an ending pointSo,The bisector of \ is: MNow,From the above figure,The bisector divided the given line segment into 2 equal parts and given the length of 1 partSo,\ = 2\Hence,The length of \ = \ + \= 2 × 2\= 2 × \= \ × \= \We can conclude that the length of \ is: \

Question 3.Identify the segment bisector of \. Then find MQ.Answer:The given figure is:We know that,A Bisector is a line that divides a line segment into 2 congruent equal partsSo,The bisector of \ is: line lWe know that,We can conclude that the value of MQ is:7

Question 4.Identify the segment bisector or \. Then find RS.Answer:

Question 5.The endpoints of \ are A and B. Find the coordinates of the midpoint M.Answer:The given endpoints of \ are:A , B We know that,M = , \)So,M = , \)M = , \)M = Hence, from the above,We can conclude that the coordinates of the midpoint of \ are:

**Don’t Miss: Geometry Basics Homework 2 Segment Addition Postulate **

## Basics Of Geometry Cumulative Assessment

Question 1.Use the diagram to determine which segments, if any, are congruent. List all congruent segments.Answer:The Congruency means having the same size and the same lengthBut, from the above coordinate plane,We can observe that there are no congruent linesHence, from the above,We can conclude that there are no congruent line segments in the coordinate plane

Question 2.Order the terms so that each consecutive term builds off the previous term.plane segment line point rayAnswer:a. Plane b. Segment c. Line d. Point e. RayHence,The order of the given terms are:Point, Line, Ray, Segment, and Plane

Question 3.The endpoints of a line segment are and . Which choice shows the correct midpoint and distance between these two points? \\) 18.8 units \\) 18.8 units \\) 9.4 units \\) 9.4 unitsAnswer:The given endpoints of a line segment are: and We know that,The coordinates of the midpoint = , \)= , \)= , \)= , 9)The distance between the coordinates = \= \= 18.78 18.8We can conclude that option shows the correct midpoint and distance

Question 4.Find the perimeter and area of the figure shownAnswer:Q , R , S , and T Now,\ = \= \= 6\ = \= \= 1\ = \= \= 6\ = \= \= 1The perimeter of the given polygon = QR + RS + ST + TQ= 6 + 1 + 6 + 1The area of the given polygon = Length × WidthSo,The area of the polygon = 6 = 6The perimeter of the given polygon is: 14The area of the given polygon is: 6

b. Identify all linear pairs.Answer:

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

Access the Big Ideas Math Geometry Ch 1 Answers for all the topics and prepare accordingly. Find complete assistance on Geometry Chapter 1 including questions from Lessons 1.1-1.6, Performance Tests, Review Tests, Cumulative Practice, Assessment Tests, etc. All you have to do is simply tap on the quick links available and clear your ambiguities in no time. To make it easy for you we have compiled the BIM Geometry Chapter 1 Basics of Geometry Textbook Solutions aligned as per the BIM Textbooks.

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

Question 13.**ABSTRACT REASONING**Describe 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

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## Exercise 16 Describing Pairs Of Angles

Vocabulary and Core Concept Check

Question 1.Explain what is different between adjacent angles and vertical angles.Answer:

**WHICH ONE DID DOESNT BELONG?**Which one does hot belong with the other three? Explain your reasoning.Answer:The angle that is the same in more than 1 angle-pair and has a common side is called Adjacent AngleSo,From the above figure,We can observe that only the first figure has an adjacent angle whereas all the three figures dont have any adjacent anglesHence, from the above,We can conclude that the first figure does not belong with the other three

Monitoring Progress and Modeling with Mathematics

In Exercises 3-6, use the figure.

Question 3.Name a pair of adjacent complementary angles.Answer:

Name a pair of adjacent supplementary angles.Answer:The angles that have the sum of the angle measures 180° are called Supplementary anglesHence, from the figure,A pair of adjacent supplementary angles are: LJN + LJK

Question 5.Name a pair of nonadjacent complementary angles.Answer:

Name a pair of nonadjacent supplementary angles.Answer:The angles that have the sum of the angle measures 180° are called Supplementary anglesHence, from the figure,A pair of adjacent supplementary angles are: LJN + LJK and NGP + HGF

In Exercises 7 10. find the angle measure.

Question 7.1 is a complement of 2, and m1 = 23°. Find, m2.Answer:

CAB = 58° and CAD = 32°

Question 13.UVW and XYZ arc complementary angles, mUVW = °. and mXYZ = °.Answer:

c. CAD EAF.

## 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

**Also Check: Mcgraw Hill Geometry Workbook Answers **

## 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.

## 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:

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