Geometry Chapter 3 Assessment Book

Study Skills: Analyzing Your Errors

Mathematical Practices

Question 1.Draw the portion of the diagram that you used to answer Exercise 26 on page 130.Answer:The portion of the diagram that you used to answer Exercise 26 on page 130 is:

Question 2.In Exercise 40 on page 144. explain how you started solving the problem and why you started that way.Answer:In Exercise 40 on page 144,You started solving the problem by considering the 2 lines parallel and two lines as transversalsSo,If p and q are the parallel lines, then r and s are the transversalsIf r and s are the parallel lines, then p and q are the transversals

Mcdougal Littell Geometry Chapter 3 Resource Book Answer Key

Geometry Terms 2 And 4

Chapter 5 Midsegments, Medians, Angles Bisectors, Perpendicular Bisectors, Altitudes

Chapter 5 Review Click HERE

Chapter 5 Review Answer Key Click HERE

Chapter 5 Review #2 Click HERE

Chapter 5 Review #2 Answer Key Click HERE

Chapter 7 Pythagorean Theorem, Special Right Triangles, and Trigonometry

Chapter 7 Review Click HERE

Chapter 7 Review Answer Key Click HERE

Cumulative Review Chapters 5 and 7

Ch 5 and 7 Cumulative Review Packet Click HERE

Ch 5 and 7 Cumulative Review Packet Answer Key Click HERE

Chapter 8 Quadrilaterals

Chapter 8 Review Click HERE

Chapter 8 Review Answer Key Click HERE

Chapter 10 Circles, Tangents, Secants, Arcs

10.1 PowerPoint Presentation Notes Click HERE

10.1 Worksheet A Click HERE

10.2 PowerPoint Presentation Notes Click HERE

10.2 Worksheet B Click HERE

10.3 PowerPoint Presentation Notes Click HERE

10.3 Worksheet A Click HERE

10.4 PowerPoint Presentation Notes Click HERE

10. 4 Inscribed Angles GeoGebra Demonstration Click HERE

10.4 Worksheet Click HERE

10.5 PowerPoint Presentation Notes Click HERE

10.5 Chord Properties Investigation Worksheet Click HERE

10.5 Chord Properties Worksheet Day 2 Click HERE

10.6 PowerPoint Presentation Notes Click HERE

10.6 Practice Examples Click HERE

10.7 PowerPoint Presentation Notes Click HERE

10.7 Worksheet A Click HERE

Chapter 10 Review Click HERE

Chapter 10 Review Answer Key Click HERE

Cumulative Review Chapters 8 and 10

11.1 Worksheet A Click HERE

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Proofs With Parallel Lines

Exploration 1

Exploring Converses

Work with a partner: Write the converse of each conditional statement. Draw a diagram to represent the converse. Determine whether the converse is true. Justify your conclusion.CONSTRUCTING VIABLE ARGUMENTSTo be proficient in math, you need to make conjectures and build a logical progression of statements to explore the truth of your conjectures.

a. Corresponding Angles Theorem : If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.Converse:If the pairs of corresponding angles are

congruent, then the two parallel lines are

cut by a transversal.

b. Alternate Interior Angles Theorem : If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.Converse:If the pairs of alternate interior angles are

congruent, then the two parallel lines are

cut by a transversal.

Answer:The converse of the Alternate Interior angles Theorem:The Converse of the Alternate Interior Angles Theorem states that if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallelSo,When we compare the actual converse and the converse according to the given statement,we can conclude that the converse we obtained from the given statement is false

are congruent, then the two parallel

lines are cut by a transversal.

are supplementary, then the two parallel lines

are cut by a transversal

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Lesson 35 Equations Of Parallel And Perpendicular Lines

Monitoring Progress

Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.

Question 1.A, B 4 to 1Answer:The given coordinates are: A , and B Compare the given points withA , and B It is given that

The coordinates of line a are: , and The coordinates of line b are: , and The coordinates of line c are: , and The coordinates of line d are: , and Now,Compare the given coordinates with , and So,The slope of line a = \= \= \

The slope of line b = \= \= \

The slope of line c = \= \= \

The slope of line d = \= \= \

The equation of the perpendicular line that passes through is:y = \x + cTo find the value of c, substitute in the above equationSo,5 = \ + cc = 5 + \c = \The equation of the perpendicular line that passes through is:y = \x + \

Question 5.How do you know that the lines x = 4 and y = 2 are perpendiculars?Answer:x = 4 and y = 2We know that,The line x = 4 is a vertical line that has the right angle i.e., 90°The line y = 4 is a horizontal line that have the straight angle i.e., 0°So,The angle at the intersection of the 2 lines = 90° 0° = 90°Hence, from the above,We can conclude that the lines x = 4 and y = 2 are perpendicular lines

Parallel And Perpendicular Lines Cumulative Assessment

Question 1.Use the steps in the construction to explain how you know that\ is the perpendicular bisector of \.Answer:Draw a line segment of any length and name that line segment as ABStep 2:Draw an arc by using a compass with above half of the length of AB by taking the center at A above ABStep 3:Draw another arc by using a compass with above half of the length of AB by taking the center at B above ABStep 4:Repeat steps 3 and 4 below ABStep 5:Draw a line segment CD by joining the arcs above and below ABStep 6:Measure the lengths of the midpoint of AB i.e., AD and DB.By measuring their lengths, we can prove that CD is the perpendicular bisector of AB

Question 2.The equation of a line is x + 2y = 10.a. Use the numbers and symbols to create the equation of a line in slope-intercept formthat passes through the point and is parallel to the given line.Answer:The given line equation is:x + 2y = 10The given point is: Now,The given equation in the slope-intercept form is:y = \x + 5We know that,The slopes of the parallel lines are the sameSo,The equation of the line that is parallel to the given line equation is:y = \x + cTo find the value of c,Substitute in the above equationSo,-5 = \ + cc = -5 + 2We can conclude that the line that is parallel to the given line equation is:y = \x 3

We can conclude that 42° and 48° are the vertical angles

Question 5.Enter a statement or reason in each blank to complete the two-column proof.Given 1 3The completed table is:

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Lesson 31 Pairs Of Lines And Angles

Monitoring Progress

Question 1.Look at the diagram in Example 1. Name the line through point F that appear skew to .From Example 1,We can observe thatThe line that passes through point F that appear skew to \ is: \

Question 2.In Example 2, can you use the Perpendicular Postulate to show that is not perpendicular to ? Explain why or why not.Answer:Perpendicular Postulate:According to this Postulate,If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given lineNow,In Example 2,We can observe that \ is not perpendicular to \ because according to the perpendicular Postulate, \ will be a straight line but it is not a straight line when we observe Example 2Hence, from the above,We can conclude that we can use Perpendicular Postulate to show that \ is not perpendicular to \

Classify the pair of numbered angles.

Question 3.

We know that,The angles that have the common side are called Adjacent anglesThe angles that are opposite to each other when 2 lines cross are called Vertical anglesSo,2 and 3 are vertical angles4 and 5 are adjacent angles1 and 8 are vertical angles2 and 7 are vertical anglesHence, from the above,We can conclude that 4 and 5 angle-pair do not belong with the other three

Monitoring Progress and Modeling with Mathematics

d. Should you have named all the lines on the cube in parts – except \? Explain.Answer:No, we did not name all the lines on the cube in parts except \

Question 30.

Parallel And Perpendicular Lines Chapter Review

3.1 Pairs of Lines and Angles

Think of each segment in the figure as part of a line. Which line or plane appear to fit the description?Question 1.

The lines that do not have any intersection points are called Parallel linesHence,The line parallel to \ is: \

Question 3.Answer:We know that,The lines that do not intersect and are not parallel and are not coplanar are Skew linesHence,From the above figure,The lines skew to \ are: \, \, \, and \

Question 4.plane parallel to plane LMQAnswer:We can conclude that the plane parallel to plane LMQ is: Plane JKL

3.2 Parallel Lines and Transversals

Find the values of x and y.

Question 5.

y = \ 3y = \The point of intersection = , \)Now,The points are: , , \)So,d = \= \= 2.12We can conclude that the distance from point A to the given line is: 2.12

Question 26.A, y = \x + 1Answer:y = \x + 1 -The given point is: A Compare the given equation withy = mx + cThe product of the slopes of the perpendicular lines is equal to -1So,) = -1m2 = -2The equation that is perpendicular to the given line equation is:y = -2x + cSubstitute A in the above equation to find the value of cSo,

The equation of the line that is perpendicular to the given line equation is:y = \x + cTo find the value of c,Substitute in the given equation2 = \ + cc = \The equation of the line that is perpendicular to the given line equation is:y = \x \

a. Find an equation of line q.Answer:The coordinates of line q are:, Compare the given points with, Slope = \= \= \

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Pairs Of Lines And Angles

Exploration 1

Points of intersection

work with a partner: Write the number of points of intersection of each pair of coplanar lines.Answer:The given coplanar lines are:a. The points of intersection of parallel lines:We know that,The Parallel lines have the same slope but have different y-interceptsSo,We can say that any parallel line do not intersect at any pointHence, from the above,We can conclude that the number of points of intersection of parallel lines is: 0

a. The points of intersection of intersecting lines:We know that,The Intersecting lines have a common point to intersectSo,We can say that any intersecting line do intersect at 1 pointHence, from the above,We can conclude that the number of points of intersection of intersecting lines is: 1

c. The points of intersection of coincident lines:We know that,The Coincident lines may be intersecting or parallelSo,We can say that any coincident line do not intersect at any point or intersect at 1 pointHence, from the above,We can conclude that the number of points of intersection of coincident lines is: 0 or 1

Exploration 2

Classifying Pairs of Lines

Exploration 3

Identifying Pairs of Angles

b. Identify all the linear pairs of angles. Explain your reasoning.Answer:A Linear pair is a pair of adjacent angles formed when two lines intersectHence, from the given figure,We can conclude that the linear pair of angles is:1 and 2 4 and 3 5 and 6 8 and 7

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Big Ideas Math Book Geometry Answer Key Chapter 3 Parallel And Perpendicular Lines

Learn the concepts quickly using the BIM Book Geometry Answer Key Chapter 3 Parallel and Perpendicular Lines. For a better learning experience, we have compiled all the Big Ideas Math Geometry Answers Chapter 3 as per the Big Ideas Math Geometry Textbooks format. You can find all the concepts via the quick links available below. Simply tap on them and learn the fundamentals involved in the Parallel and Perpendicular Lines Chapter.

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Parallel And Perpendicular Lines Maintaining Mathematical Proficiency

Find the slope of the line.

Question 1.From the given coordinate plane,Let the given points are:A , and B Compare the given points withA , B We know that,Slope of the line = \So,Slope of the line = \= \We can conclude that the slope of the given line is: \

Question 2.From the given coordinate plane,Let the given points are:A , and B Compare the given points withA , B We know that,Slope of the line = \So,Slope of the line = \= \We can conclude that the slope of the given line is: 3

Question 3.From the given coordinate plane,Let the given points are:A , and B Compare the given points withA , B We know that,Slope of the line = \So,Slope of the line = \= \Hence, from the above,We can conclude that the slope of the given line is: 0

Write an equation of the line that passes through the given point and has the given slope.

Question 4.

The equation of the line along with y-intercept is:y = \x + 9

Question 10.ABSTRACT REASONINGWhy does a horizontal line have a slope of 0, but a vertical line has an undefined slope?Answer:Slope of the line = \We know that,The coordinates of y are the same. i.e.,y1 = y2 = y3 The coordinates of x are the same. i.e.,x1 = x2 = x3 .The slope of the horizontal line = \We know that,Any fraction that contains 0 in the numerator has its value equal to 0So,The slope of horizontal line = 0The slope of vertical line = \We know that,Any fraction that contains 0 in the denominator has its value undefinedSo,The slope of the vertical line = Undefined

Why To Read Geometry Bigideas Math Answer Key

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Exercise 34 Proofs With Perpendicular Lines

Vocabulary and core Concept Check

Question 1.COMPLETE THE SENTENCEThe perpendicular bisector of a segment is the line that passes through the _______________ of the segment at a _______________ angle.Answer:

The given figure is:Now,Using P as the center and any radius, draw arcs intersecting m and label those intersections as X and Y.Using X as the center, open the compass so that it is greater than half of XP and draw an arc.Using Y as the center and retaining the same compass setting, draw an arc that intersects with the firstLabel the point of intersection as Z. Draw \

CONSTRUCTIONIn Exercises 9 and 10, trace \. Then use a compass and straightedge to construct the perpendicular bisector of \

Question 9.

We know that,According to the Perpendicular Transversal theorem,The distance from the perpendicular to the line is given as the distance between the point and the non-perpendicular lineSo,From the given figure,The distance from point C to AB is the distance between point C and A i.e., ACHence, from the above,We can conclude that the distance from point C to AB is: 12 cm

PROVING A THEOREM In Exercises 13 and 14, prove the theorem.Question 13.Linear Pair Perpendicular Theorem Answer:

Lines Perpendicular to a Transversal Theorem Answer:In a plane, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line alsoProof:Given: k || l, t kProve: t l

In Exercises 15 and 16, use the diagram to write a proof of the statement.

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Lesson 32 Parallel Lines And Transversals

Monitoring Progress

Use the diagram

Question 1.Given m1 = 105°, find m4, m5, and m8. Tell which theorem you use in each case.Answer:It is given that 1 = 105°Now,We have to find 4, 5, and 8Now,To find 4:Verticle angle theorem:Vertical Angles Theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruentSo,

We can conclude that the value of x is: 54°

Question 3.In the proof in Example 4, if you use the third statement before the second statement. could you still prove the theorem? Explain.Answer:In Example 4, the given theorem is Alternate interior angle theoremIf you even interchange the second and third statements, you could still prove the theorem as the second line before interchange is not necessaryHence, from the above,We can conclude that if you use the third statement before the second statement, you could still prove the theorem

Question 4.WHAT IF?In Example 5. yellow light leaves a drop at an angle of m2 = 41°. What is m1? How do you know?Answer:If we observe 1 and 2, then they are alternate interior anglesNow,According to Alternate interior angle theorem,1 = 2

1 = 2 = 133° and 3 = 47°

Question 13.Describe and correct the error in the students reasoningAnswer:

b. Name two pairs of supplementary angles when \ and \ are parallel. Explain your reasoning.Answer:From the given figure,The two pairs of supplementary angles when \ and \ are parallel is: ACD and BDC

Question 21.