## Lesson 12 Measuring And Constructing Segments

**Monitoring Progress**

Use a ruler to measure the length of the segment.

Question 1.The length of the given segment in cm is:

Question 2.The length of the given line segment in cm is:

Question 3.The length of the given line segment in cm is:

Question 4.The length of the given line segment in cm is:

Question 5.Plot A, B, C, and D in a coordinate plane. Thendetermine whether \ and \ are congruent.Answer:A , B , C , and D We know that,The distance between 2 points is:d = ² + ²Now,The representation of the given points in the coordinate plane is:Now,The distance between AB = ² + ²= 0 + 5²The distance between CD = ² + ²= 0 + 4²Since the distance between \ and \ are not same,\ is not congruent to \Hence,\ \

Question 6.Use the Segment Addition Postulate to find XZ.Answer:The given figure is:We know that,The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equationAB + BC = ACWe can conclude that the value of XZ is: 73

The length of the given line segment is:

**CONSTRUCTION**In Exercises 7 and 8. use a compass and straightedge to construct a copy of the segment.Question 7.Copy the segment in Exercise 3.Answer:

In Exercises 9 14, plot the points in a coordinate plane. Then determine whether \ and \ are congruent.Question 9.A, B, C, DAnswer:

Question 11.A, B, C, DAnswer:

Question 13.A, B, C, DAnswer:

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## 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:

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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.

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## Lesson 15 Measuring And Constructing Angles

Monitoring Progress

Write three names for the angle.

Question 1.An Angle is formed when two rays have the same endpoint or vertex.So,Here, the angle is QHence,The three names for the given angle are: Q, PQR, and RQP

Question 2.An Angle is formed when two rays have the same endpoint or vertex.So,Here, the angle is YHence,The three names for the given angle are: 1, XYZ, and ZYX

Question 3.An Angle is formed when two rays have the same endpoint or vertex.So,Here, the angle is EHence,The three names for the given angle are: 2, FED, and DEF

Use the diagram in Example 2 to find the angle measure. Then classify the angle.

Question 4.

EFH and HFG are 60° and 30° respectively

Question 10.Angle MNP is a straight angle, and \Q bisects MNP. Draw MNP and \Q. Use arcs to mark the congruent angles in your diagram. Find the angle measures of these congruent angles.Answer:It is given that angle MNP is a straight angle, and \Q bisects MNP. Draw MNP and \Q.So,The representation of the above statement is:Hence, from the above,We can conclude that the angle measure of each congruent angle is: 55.3°

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## Perimeter And Area In The Coordinate Plane

**Essential Question**

How can you find the perimeter and area of a polygon in a coordinate plane?Answer:When two-dimensional figures are shown on the coordinate plane, a mix of counting and the Pythagorean Theorem can be used to determine the lengths of each side. Then add up the lengths to determine the perimeter or use the basic area formulas for triangles and rectangles to determine the area of the figure.

**Exploration 1**

Finding the Perimeter and Area of a Quadrilateral

Work with a partner

a. On a piece of centimeter graph paper. draw quadrilateral ABCD in a coordinate plane. Label the points A, B C, and D.Answer:A , B , C , and D Hence,The representation of the given points in the coordinate plane are:

b. Find the perimeter of quadrilateral ABCD.Answer:A , B , C , and D We know that,The perimeter is defined as the sum of all the sides of a polygonSo,In a coordinate plane, the perimeter of the polygon can be found by finding the lengths of the given sidesWe know that,The length of the side of a polygon in a coordinate plane is:D = \So,AB = \= \The perimeter of the Quadrilateral ABCD = AB + BC + CD + DA= 5 + 5 + 5 + 5

**Exploration 2**

Finding the Area of a Polygon Work with a partner.

The area of BPA:The length of BP = \= \= 4The length of PA = \= \= 3The length of BA = \= \= 5The area of BPA = \ × Base × Height= \ = 6

The area of DRC:The length of DR = \= \= 4The length of RC = \= \= 3The length of CD = \= \= 5The area of DRC = \ × Base × Height= \ = 6

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## 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 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 PRECISION**To 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

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