Big Ideas Math Book Geometry Answer Key Chapter 3 Parallel And Perpendicular Lines
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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
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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
Exercise 35 Equations Of Parallel And Perpendicular Lines
Vocabulary and Core Concept Check
Question 1.COMPLETE THE SENTENCEA _________ line segment AB is a segment that represents moving from point A to point B.Answer:
How are the slopes of perpendicular lines related?Answer:We know that,The Perpendicular lines are lines that intersect at right angles.If you multiply the slopes of two perpendicular lines in the plane, you get 1 i.e., the slopes of perpendicular lines are opposite reciprocals
Monitoring Progress and Modeling with Mathematics
In Exercises 3 6. find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.
Question 3.A, B 1 to 4Answer:
A, B 3 to 2Answer: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 parallel lines have the same slopesThe perpendicular lines have the product of slopes equal to -1Hence, from the above,Line c and Line d are parallel linesLine b and Line c are perpendicular lines
In Exercises 9 12, tell whether the lines through the given points are parallel, perpendicular, or neither. justify your answer.
Question 9.Line 1: , Line 2: , Answer:
Question 11.Line 1: , Line 2: , Answer:
Question 33.
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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.
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
Communicate Your Answer
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Parallel Lines And Transversals
Exploration 1
Exploring parallel Lines
Work with a partner: Use dynamic geometry software to draw two parallel lines. Draw a third line that intersects both parallel lines. Find the measures of the eight angles that are formed. What can you conclude?Answer:By using the dynamic geometry,The representation of the given coordinate plane along with parallel lines is:Hence, from the coordinate plane,We can observe that,3 = 53.7° and 4 = 53.7°We know that,The angle measures of the vertical angles are congruentSo,1 = 53.7° and 5 = 53.7°We know that,All the angle measures are equalHence, from the above,1 = 2 = 3 = 4 = 5 = 6 = 7 = 53.7°
Exploration 2
Writing conjectures
Work with a partner. Use the results of Exploration 1 to write conjectures about the following pairs of angles formed by two parallel lines and a transversal.ATTENDING TO PRECISIONTo be proficient in math, you need to communicate precisely with others.a. corresponding anglesAnswer:We know that,When two lines are crossed by another line , the angles in matching corners are called Corresponding anglesHence, from the given figure,We can conclude thatThe corresponding angles are: and 5 4 and 8
b. alternate interior anglesAnswer:We know that,Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.Hence, from the above figure,We can conclude thatThe alternate interior angles are: 3 and 5 2 and 8
Communicate Your Answer
Mcdougal Littell Geometry Practice Workbook
1st Edition
Boswell, Larson, Stiff, Timothy D. Kanold
ISBN: 9780618736959
Boswell, Larson, Stiff, Timothy D. Kanold
ISBN: 9780618736959
At Quizlet, were giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from McDougal Littell Geometry Practice Workbook 1st Edition, youll learn how to solve your toughest homework problems. Our resource for McDougal Littell Geometry Practice Workbook includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With expert solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence.
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Parallel And Perpendicular Lines Mathematical Practices
Use a graphing calculator to graph the pair of lines. Use a square viewing window. Classify the lines as parallel, perpendicular, coincident, or non-perpendicular intersecting lines. Justify your answer.
Question 1.The representation of the given pair of lines in the coordinate plane is:We know that,For a pair of lines to be perpendicular, the product of the slopes i.e., the product of the slope of the first line and the slope of the second line will be equal to -1So,By comparing the given pair of lines withy = mx + bThe slope of first line = \The slope of second line = 2So,m1 ×m2 = \ × 2= -1We can conclude that the given pair of lines are perpendicular lines
Question 2.
The representation of the given pair of lines in the coordinate plane is:
We know that,For a pair of lines to be non-perpendicular, the product of the slopes i.e., the product of the slope of the first line and the slope of the second line will not be equal to -1So,By comparing the given pair of lines withy = mx + bThe slope of first line = \The slope of second line = 1So,m1 ×m2 = \Hence, from the above,We can conclude that the given pair of lines are non-perpendicular lines
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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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.
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Mathematical Practices
Question 1.Compare the effectiveness of the argument in Exercise 24 on page 153 with the argument You can find the distance between any two parallel lines What flaw exist in the argument? Does either argument use correct reasoning? Explain.Answer:From the argument in Exercise 24 on page 153,We can say thatThe claim of your friend is not correctWe know that,If we want to find the distance from the point to a given line, we need the perpendicular distance of a point and a lineHence, from the above,We can conclude that we can not find the distance between any two parallel lines if a point and a line is given to find the distance
Question 2.Look back at your construction of a square in Exercise 29 on page 154. How would yourconstruction change if you were to construct a rectangle?Answer:From the construction of a square in Exercise 29 on page 154,We can observe that the length of all the line segments are equalNow,If you were to construct a rectangle,We have to keep the lengths of the length of the rectangles the same and the widths of the rectangle also the same
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Faqs On High School Bim Textbook Geometry Answers
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Proofs With Perpendicular Lines
Exploration 1
Writing Conjectures
Work with a partner: Fold a piece of pair in half twice. Label points on the two creases. as shown.a. Write a conjecture about \ and \. Justify your conjecture.Answer:The conjecture about \ and \ is:If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
b. Write a conjecture about \ and \ Justify your conjecture.Answer:The conjecture about \ and \ is:In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
Exploration 2
Exploring a segment Bisector
Work with a partner: Fold and crease a piece of paper. as shown. Label the ends of the crease as A and B.a. Fold the paper again so that point A coincides with point B. Crease the paper on that fold.Answer:
b. Unfold the paper and examine the four angles formed by the two creases. What can you conclude about the four angles?Answer:When we unfold the paper and examine the four angles formed by the two creases, we can conclude that the four angles formed are the right angles i.e., 90°
Exploration 3
Communicate Your Answer
Question 5.In Exploration 3. find AO and OB when AB = 4 units.Answer:
We can conclude that the distance from point E to \ is: 7.07
Use the lines marked in the photo.
Question 3.Is b || a? Explain your reasoning.Answer:There is not any intersection between a and bHence, from the above,We can conclude that b || a
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