Savvas Learning Co Geometry Student Edition Chapter 3 Parallel and Perpendicular Lines Exercise 3.1 Lines And Angles
Savvas Learning Co Geometry Student Edition Chapter 3 Exercise 3.1 Lines And Angles Solutions Page 143 Exercise 1 Problem 1
Given: A figure.
To Find – Parallel segments in the given figure.A segment is a part of the line.
We have a figure
In the given figure, we can see that the parallel segments are
The parallel segments in the given figure are
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Exercise 3.1 Lines And Angles Savvas Geometry Answers Page 143 Exercise 2 Problem 2
Given: A figure.
To Find – Skew segments in the given figure.
A segment is a part of the line.
We have a figure
In the given figure, we can see that skew segments are
Some possible pairs of skew segments in the given figure are
Exercise 3.1 Lines And Angles Savvas Geometry Answers Page 143 Exercise 3 Problem 3
Some possible parallel planes in the given figure are:
Plane EFGH ∥ Plane ABCD
Plane AEFB ∥ Plane DHGC
Plane AEHD ∥ Plane BFGC
Lines And Angles Solutions Chapter 3 Exercise 3.1 Savvas Geometry Page 143 Exercise 4 Problem 4
Given: A figure.
To Find – Alternate interior angles in the given figure.
An angle is a combination of two rays ( half-lines ) with a common endpoint.
We have a figure
In the given figure, we can see that the possible pairs of alternate interior angles are
⇒ ∠2 and ∠3
⇒ ∠8 and ∠6
The possible pairs of alternate interior angles in the given figure are: ∠2 and ∠3, ∠8 and ∠6
Lines And Angles Solutions Chapter 3 Exercise 3.1 Savvas Geometry Page 143 Exercise 5 Problem 5
Given: A figure.
To Find – Same-side interior angles in the given figure.
An angle is a combination of two rays ( half-lines ) with a common endpoint.
We have a figure
In the given figure, we can see that the pairs of same-side interior angles are
⇒ ∠3 and ∠8
⇒ ∠6 and ∠2
The possible pairs of same-side interior angles are: ∠3 and ∠8, ∠6 and ∠2
Chapter 3 Exercise 3.1 Lines And Angles Savvas Learning Co Geometry Explanation Page 143 Exercise 6 Problem 6
Given: A figure.
To Find – Corresponding angles in the given figure.
An angle is a combination of two rays ( half-lines ) with a common endpoint.
We have a figure
In the given figure, we can see the possible pairs of the corresponding angles are
⇒ ∠1 and ∠3
⇒ ∠7 and ∠6
⇒ ∠8 and ∠5
⇒ ∠2 and ∠4
The possible pairs of the corresponding angles are: ∠1 and ∠3,∠7 and ∠6,∠8 and ∠5,∠2 and ∠4
Solutions For Lines And Angles Exercise 3.1 In Savvas Geometry Chapter 3 Student Edition Page 143 Exercise 7 Problem 7
Given: A figure.
To Find – Alternate exterior angles in the given figure.
An angle is a combination of two rays ( half-lines ) with a common endpoint.
We have a figure
In the given figure, we can see that possible pairs of alternate exterior angles are
⇒ ∠1 and ∠4
⇒ ∠7 and ∠5
The possible pairs of the alternate exterior angles in the given figure are:∠1 and ∠4, ∠7 and ∠5
Solutions for Lines and Angles Exercise 3.1 in Savvas Geometry Chapter 3 Student Edition Page 143 Exercise 8 Problem 8
Parallel lines are the lines that do not intersect, and if we do not include the property of coplanarity, we can find the lines in different planes , and will be called skew lines.
Skew lines are the lines that do not intersect but are not in the same plane, thus parallel lines are coplanar and which do not meet.
Coplanar is included in the definition of parallel planes to differentiate from the definition of skew lines.
Exercise 3.1 Lines And Angles Savvas Learning Co Geometry Detailed Answers Page 143 Exercise 9 Problem 9
Alternate interior angles are formed by a transversal intersecting two lines.
The angles are located inside the two lines but on the opposite sides of the transversal.
Alternate interior angles are located inside the two parallel lines on the opposite sides of the transversal.
Exercise 3.1 Lines And Angles Savvas Learning Co Geometry Detailed Answers Page 143 Exercise 10 Problem 10
Given: A figure is given
To Find – Who is correct between Juan and Carly?
As the question says lines appearing to be parallel are parallel.
In the figure, it can be seen clearly that AB ∥ HG
Since Carly is saying AB ∥ HG, that is correct.
But Juan is saying that AB and HG are skewed, so he is wrong.
Carly is correct because he is saying AB∥HG
Geometry Chapter 3 Lines And Angles Savvas Learning Co Explanation Guide Page 144 Exercise 11 Problem 11
Given: A figure is given
To Find – All lines that are parallel to AB
In the figure, a line that is parallel to AB is FG
Line parallel to AB is FG
Geometry Chapter 3 Lines And Angles Savvas Learning Co Explanation Guide Page 144 Exercise 12 Problem 12
Given: A figure is given
To Find – All lines that are parallel to DH
In the figure, lines that are parallel to DH are GB, FA, JE, and CL
Lines parallel to DH are GB, FA, JE, and CL
Savvas Learning Co Geometry Student Edition Chapter 3 Page 144 Exercise 13 Problem 13
Given: A figure is given
To Find – All lines that are parallel to EJ
In the figure, lines that are parallel to EJ are FA, GB, DH, and CL.
Lines parallel to EJ FA, GB, DH, and CL
Page 144 Exercise 14 Problem 14
Given: A figure is given
To Find – All lines that are parallel to the plane JF AE
Lines parallel to JF AE are GB, DH, and CL
Savvas Learning Co Geometry Student Edition Chapter 3 Page 144 Exercise 15 Problem 15
Given: A figure is given
To Find – A plane parallel to LH
A plane parallel to LH is JFGDC
Page 144 Exercise 16 Problem 16
Given: A figure is given
To Find – Alternate interior angles.
Alternate interior angles in the figure are 2 & 3
Savvas Learning Co Geometry Student Edition Chapter 3 Page 144 Exercise 17 Problem 17
Given: A figure is given
To Find – Whether the angles labeled in the same color alternate interior angles, same-side interior angles, corresponding angles, or alternate exterior angles?
Angles 3 & 4 and 5 & 6 are corresponding angles and angles 1 & 2 are same side interior angles.
Page 144 Exercise 18 Problem 18
Given: A figure is given
To Find – Whether the angles labeled in the same color alternate interior angles, same-side interior angles, corresponding angles, or alternate exterior angles?
Only angles 5 & 6 are alternate interior angles.
Savvas Learning Co Geometry Student Edition Chapter 3 Page 144 Exercise 19 Problem 19
Given: A figure is given
To Find – Whether ∠1 & ∠2 are alternate interior angles, same-side interior angles, corresponding angles, or alternate exterior angles?
∠1 & ∠2 are corresponding angles.
Page 144 Exercise 20 Problem 20
Let, the lines p,q be cut by a transversal t.
Clearly,∠1 & ∠8 and ∠5 & ∠4 forms the pair of alternate exterior angles.
Two pairs of alternate exterior angles do two lines and a transversal form.
Savvas Learning Co Geometry Student Edition Chapter 3 Page 144 Exercise 21 Problem 21
Given: \(\stackrel{\leftrightarrow}{E D} \| \overleftarrow{H} \hat{G}\)
To find – The statement as true or false.
The lines are False they are making skew lines.
According to the figure given, we can say that \(\overleftrightarrow{E D}\) ∦ \(\overleftarrow{H} \hat{G}\) the lines and planes that appear to be parallel are not parallel they are skew.
Page 145 Exercise 22 Problem 22
Given: Plane AED∥ Plane FGH
To find – The statement as true or false.
The plane AED∥ plane FGH is true.
According to the figure given, we can say that plane AED∥ plane FGH. The lines and planes that appear to be parallel are parallel.
Savvas Learning Co Geometry Student Edition Chapter 3 Page 145 Exercise 23 Problem 23
Given: Plane ABH ∥ Plane CDF
To find – The statement as true or false.
The lines are False they intersect above \(\overrightarrow{C G}\)
According to the figure given, we can say that plane ABH ∥ plane CDF the lines and planes that appear to be parallel are not parallel they intersect above \(\overrightarrow{C G}\)
Page 145 Exercise 24 Problem 24
Given: \(\overrightarrow{A B}\) and \(\overrightarrow{H G}\) are skew line
To find – The statement as true or false.
The lines are skew lines.
According to the figure given, we can say that \(\overrightarrow{A B}\) and \(\overrightarrow{H G}\) the lines and planes appear to be a skew line.
Savvas Learning Co Geometry Student Edition Chapter 3 Page 145 Exercise 25 Problem 25
Given: \(\overrightarrow{A E}\) and \(\overrightarrow{B C}\) are skew line
To find – The statement as true or false.
The lines are not skew lines because they intersect at point A.
According to the figure given, we can say that \(\overrightarrow{A E}\) and \(\overrightarrow{B C}\) the lines and planes apperear to be is not a skew lines because they intersect at point A.
Page 145 Exercise 26 Problem 26
Given: A rectangular rug covers the floor in a living room.
One of the walls in the same living room is painted blue.
To find – Are the rug and the blue wall parallel No, the rug and the blue wall are not parallel because they intersect.
The opposite wall can be parallel to the blue wall.
A rectangular rug covers the floor in a living room. One of the walls in the same living room is painted blue is not parallel because they intersect.
Savvas Learning Co Geometry Student Edition Chapter 3 Page 145 Exercise 27 Problem 27
Given: Two planes that do not intersect are parallel.
To find – Determine each statement is always, sometimes, or never true.
Two planes that do not intersect are always parallel as a plane is a flat, two-dimensional surface that extends infinitely far.
A plane is the two-dimensional analog of a point, a line, and three-dimensional space.
The two planes that do not intersect are always parallel.
Page 145 Exercise 28 Problem 28
Given: A statement – Two lines that lie in parallel planes are parallel.
To find – Each statement is always, sometimes, or never true.
In order to be parallel, the two lines must be co-planer.
And as only some lines in two parallel planes are co-planer, the statement is sometimes true.
The given statement is sometimes true.