Unit 3 parallel and perpendicular lines homework 2 parallel lines cut by a transversal answer key

Priority Standard: G-C0.9: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a traversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segments's endpoint.

Topics and "I can" Statements:

I can identify corresponding, alternating interior, alternate exterior and consecutive interior angles using parallel lines and a transversal.
I can apply the relationships between corresponding, alternating interior, alternate exterior and consecutive interior angles to find unknown angle measures.
I can use angle relationships to prove that lines are parallel.
I can prove lines perpendicular and parallel.
I can find slopes given a graph or two ordered pair.
I can identify parallel and perpendicular slopes.
I can find equations of lines in slope-intercept form.

Unit 3: Parallel and Perpendicular Lines Resources
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Unit 3: Parallel and Perpendicular Lines Note Packet: Blank Copy

Unit 3- Section #1: Identify Pairs of Angles and Identify Pairs of Angles using Lines and Transversals (pg. 2-5)
Identify Pairs of Angles and Identify Pairs of Angles using Lines and Transversals Lesson: Guided Notes
Lesson Videos:
Vocabulary/Example #1 (pg. 12-13)
Vocabulary/Definitions/Theorems
Examples #2-#4
Example #5 and #6
Unit 3- Worksheet #1: Identify Pairs of Angles/Identify Pairs of Angles using Lines and Transversals
Unit 3- Worksheet #1: Answer Key

Unit 3- Section #3: Prove Lines are Parallel (pg. 6-8)
Prove Lines are Parallel Lesson: Guided Notes
Lesson Videos:
Vocabulary/Definitions/Theorems
Examples #1-4
Unit 3- Worksheet #2: Prove Lines are Parallel
Unit 3- Worksheet #2: Answer Key

Unit 3- Section #4: Prove Theorems about Perpendicular Lines (pg. 8-9)
Prove Theorems about Perpendicular Lines Lesson: Guided Notes
Lesson Videos:
Prove Theorems about Perpendicular Lines Lesson
Unit 3- Worksheet #3: Prove Theorems about Perpendicular Lines
Unit 3- Worksheet #3: Answer Key

Unit 3- Section #4: Find and Use Slopes of Lines (pg. 10-12)
Find and Use Slopes of Lines Lesson: Guided Notes
Lesson Videos:
Review
Unit 3- Worksheet #4: Find and Use Slopes of Lines
Unit 3- Worksheet #4: Answer Key

Unit 3- Section #5: Writing and Graphing Equations (pg. 13-16)
Writing and Graphing Equations Lesson: Guided Notes
Lesson Videos:
Review
Unit 3- Worksheet #5: Writing and Graphing Equations
Unit 3- Worksheet #5: Answer Key

Unit 3- Review Material
Unit 3- Parallel and Perpendicular Lines: Assessment Review
Unit 3- Parallel and Perpendicular Lines Assessment Review: Answer Key

Textbook Solutions
Class 8
Math
parallel lines and transversal

Mathematics Solutions Solutions for Class 8 Math Chapter 2 Parallel Lines And Transversal are provided here with simple step-by-step explanations. These solutions for Parallel Lines And Transversal are extremely popular among Class 8 students for Math Parallel Lines And Transversal Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Solutions Book of Class 8 Math Chapter 2 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Mathematics Solutions Solutions. All Mathematics Solutions Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Page No 8:

Question 1:

In the adjoining figure, each angle is shown by a letter. Fill in the boxes with the help of the figure.

Corresponding angles.
(1) ∠p and ☐
(2) ∠q and ☐
(3) ∠r and ☐
(4) ∠s and ☐

Interior alternate angles.
(5) ∠s and ☐
(6) ∠w and ☐

Answer:

Corresponding angles : If the arms on the transversal of a pair of angles are in the same direction and the other arms are on the same side of transversal, then it is called a pair of corresponding angles.

Corresponding angles
(1) ∠p and ∠w
(2) ∠q and ∠x
(3) ∠r and ∠y
(4) ∠s and ∠z

Alternate interior angles : A pair of angles which are on the opposite side of the transversal and inside the given lines that are intersected by the transversal.

Interior alternate angles
(5) ∠s and ∠x
(6) ∠w and ∠r

Page No 8:

Question 2:

Observe the angles shown in the figure and write the following pair of angles.

(1) Interior alternate angles
(2) Corresponding angles
(3) Interior angles

Answer:

(1) Alternate interior angles : A pair of angles which are on the opposite side of the transversal and inside the given lines that are intersected by the transversal.

Interior alternate angles
(a) ∠c and ∠e
(b) ∠b and ∠h

(2) Corresponding angles : If the arms on the transversal of a pair of angles are in the same direction and the other arms are on the same side of transversal, then it is called a pair of corresponding angles.

Corresponding angles
(a) ∠d and ∠h
(b) ∠c and ∠g
(c) ∠a and ∠e
(d) ∠b and ∠f

(3) Interior angles : A pair of angles which are on the same side of transversal and inside the given lines that are intersected by the transversal.

Interior angles
(a) ∠c and ∠h
(b) ∠b and ∠e

Page No 11:

Question 1:

1. Choose the correct alternative.
(1) In the adjoining figure, if line m ∥ line n and line p is a transversal then find x.

(A) 135°
(B) 90°
(C) 45°
(D) 40°

(2) In the adjoining figure, if line a ∥ line b and line l is a transversal then find x.

(A) 90°
(B) 60°
(C) 45°
(D) 30°

Answer:

(1)

Let us mark the points P and Q on m; R and S on n; A and B on p.
Suppose PQ and AB intersect at M; RS and AB intersect at N.
Since, m||n and p is a transversal, then
m∠QMN + m∠SNM = 180° (Interior angles on the same side of transversal are supplementary)
Substituing the values in the above equation, we get
3x + x = 180°
⇒ 4x = 180°
⇒ x = 180°4
∴ x = 45°
So, the correct answer is option (C).

(2)

Let us mark the points P and Q on a; R and S on b; A and B on l.
Suppose PQ and AB intersect at M; RS and AB intersect at N.
Since a||b and l is a transversal, then
m∠RNM = m∠SNB (Vertically opposite angles)
⇒ ∠RNM = 2x
Now, m∠RNM + m∠PMN = 180° (Interior angles on the same side of transversal are supplementary)
⇒ 2x + 4x = 180°
⇒ 6x = 180°
⇒ x = 180°6
⇒ x = 30°
So, the correct answer is option (D).

Page No 11:

Question 2:

In the adjoining figure line p ∥ line q. Line t and line s are transversals. Find measure of ∠x and ∠y using the measures of angles given in the figure.

Answer:

Let us mark the points P and Q on p; R and S on q; A and B on t; C and D on s.
Suppose PQ and AB intersect at K; PQ and CD intersect at X.
Suppose RS and AB intersect at L; RS and CD intersect at Y.
Since, AB is a straight line and ray KQ stands on it,
m∠AKX + m∠XKL = 180° (angles in linear pair)
⇒ 40° + m∠XKL = 180°
⇒ m∠XKL = 180° − 40°
⇒ m∠XKL = 140°
Since, p||q and t is a transversal, then
m∠YLB = m∠XKL (Corresponding angles)
⇒ x = 140°
Since, RS and CD are two straight lines intersecting at Y, then
m∠XYL = m∠SYD (Vertically opposite angles)
⇒ m∠XYL = 70°
Since, p||q and s is a transversal, then
m∠KXY + m∠XYL = 180° (Interior angles on same side of transversal are supplementary)
⇒ y + 70° = 180°
⇒ y = 180° − 70°
⇒ y = 110°

Page No 12:

Question 3:

In the adjoining figure. line p ∥ line q. line l ∥ line m. Find measures of ∠a, ∠b and ∠c, using the measures of given angles. Justify your answers.

Answer:

Let us mark the points A and B on p; X and Y on q; P and Q on l; R and S on m.
Suppose AB and XY intersect PQ at K and L respectively.
Suppose AB and XY intersect RS at N and M respectively.
Since, p||q and l is a transversal, then
m∠AKL + m∠XLK = 180° (Interior angles on same side of transversal are supplementary)
⇒ 80° + m∠XLK = 180°
⇒ m∠XLK = 180° − 80°
⇒ m∠XLK = 100°
Since, PQ and XY are straight lines that intersect at L, then
m∠QLM = m∠XLK (Vertically opposite angles)
⇒ a = 100°
Since, l||m and p is a transversal, then
m∠BNR = m∠AKL (Alternate exterior angles)
⇒ c = 80°
Since, p||q and m is a transversal, then
m∠NMY= m∠RNB (Corresponding angles)
⇒ b = c
⇒ b = 80°

Page No 12:

Question 4:

In the adjoining figure, line a ∥ line b. Line l is a transversal. Find the measures of ∠x, ∠y, ∠z using the given information.

Answer:

Let us mark the points A and B on l; K and M on a; L and N on b.
Suppose KM and LN intersect AB at P and Q respectively.
Since, a||b and l is a transversal, then
m∠PQL = m∠APK (Corresponding angles)
⇒ x = 105°
Since, AB and LN are straight lines that intersect at Q, then
m∠BQN = m∠PQL (Vertically opposite angles)
⇒ y = x
⇒ y = 105°
Since, AB is a straight line and ray QN stands on it, then
m∠BQN + m∠PQN = 180° (Angles in linear pair)
⇒ y + m∠PQN = 180°
⇒ 105° + m∠PQN = 180°
⇒ m∠PQN = 180° − 105°
⇒ m∠PQN = 75°
Now, m∠APM = m∠PQN (Corresponding angles)
⇒ z = 75°

Page No 12:

Question 5:

In the adjoining figure, line p ∥ line l ∥ line q. Find ∠x with the help of the measures given in the figure.

Answer:

Let us mark the points A, L and B on p; C, M and D on l; P, N and Q on q.
Since, AB||CD and LM is a transversal intersecting AB at L and CD at M, then
m∠LMD = m∠ALM (Alternate interior angles)
⇒ m∠LMD = 40°
Since, CD||PQ and MN is a transversal intersecting CD at M and PQ at N, then
m∠DMN = m∠PNM (Alternate interior angles)
⇒ m∠DMN = 30°
Now, m∠LMD + m∠DMN = 40° + 30°
⇒ m∠LMN = 70°
⇒ x = 70°

Page No 13:

Question 1:

Draw a line l. Take a point A outside the line. Through point A draw a line parallel to line l.

Answer:

Steps of construction :
(1) Draw a line l. Take a point A outside the line l.
(2) Draw a segment AM ⊥ line l.
(3) Take another point N on line l.
(4) Draw a segment NB ⊥ line l, such that l(NB) = l(MA).
(5) Draw a line m passing through the points A and B.
Hence, the line m is the required line that passes through point A and parallel to line l.

Page No 13:

Question 2:

Draw a line l. Take a point T outside the line. Through point T draw a line parallel to line l.

Answer:

Steps of construction :
(1) Draw a line l. Take a point T outside the line l.
(2) Draw a segment MT ⊥ line l.
(3) Take another point N on line l.
(4) Draw a segment NV ⊥ line l, such that l(NV) = l(MT).
(5) Draw a line m passing through the points T and V.
Hence, the line m is the required line that passes through point T and parallel to line l.

Page No 13:

Question 3:

Draw a line m. Draw a line n which is parallel to line m at a distance of 4 cm from it.

Answer:

Steps of construction :
(1) Draw a line m.
(2) Take two points A and B on the line m.
(3) Draw perpendiculars to the line m at A and B.
(4) On the perpendicular lines, take points P and Q at a distance of 4 cm from A and B respectively.
(5) Draw a line n passing through the points P and Q.
So, line n is the required line parallel to the line m at a distance of 4 cm away from it.

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