Problem 1 :
In the diagram given below, lines m, n and k represent three of the oars. If m||n and n||k, then prove m||k.
Problem 2 :
In the diagram given below, if ∠1 ≅ ∠2, then prove m||n.
Problem 3 :
In the diagram given below, each line is parallel to the next immediate line. Explain why the line K_{1} is parallel to the line K_{2}.
Problem 4 :
In the diagram given below, lines a and b are perpendicular to the line c. Prove that the lines a and b are parallel.
Problem 5 :
In the diagram given below, if ∠4 and ∠5 are supplementary, then prove g||h.
Problem 6 :
In the diagram given below, find the value of x that makes j||k.
Problem 7 :
If two boats sail at a 45° angle to the wind as shown, and the wind is constant, will their paths ever cross ? Explain.
Problem 8 :
In the diagram given below, decide which rays are parallel.
(i) Is EB parallel to HD?
(ii) Is EA parallel to HC?
1. Answer :
Statements m||n ∠1 ≅ ∠2 n||k ∠2 ≅ ∠3 ∠1 ≅ ∠3 m||k |
Reasons Given Corresponding angles postulate Given Corresponding angles postulate Transitive property of congruence Corresponding angle converse |
2. Answer :
Statements ∠1 ≅ ∠2 ∠2 ≅ ∠3 ∠1 ≅ ∠3 m||n |
Reasons Given Vertical angles theorem Transitive property of congruence Corresponding angles converse |
3. Answer :
We are given that K_{1}||K_{2 }and K_{2}||K_{3.}
By transitive property of parallel lines, K_{1}||K_{3.}
Since K_{1}||K_{3 }and K_{3}||K_{4}, again by transitive property, it follows that K_{1}||K_{4.}
4. Answer :
Since the line c cuts both the lines a and b, the line c is transversal. Both the lines a and b are perpendicular to the line c. So, the measure of both ∠1 and ∠2 in the above diagram is 90° and c is transversal to the lines a and b.
That is,
m∠1 = 90°
m∠2 = 90°
By corresponding angles converse, the lines a and b are parallel.
5. Answer :
We are given that ∠4 and ∠5 are supplementary. By the linear pair postulate, ∠5 and ∠6 are also supplementary, because they form a linear pair. By the congruence supplements theorem, it follows that ∠4 ≅ ∠6. Therefore, by the alternate interior angles converse, g and h are parallel.
6. Answer :
Lines j and k will be parallel if the marked angles are supplementary.
x° + 4x° = 180°
5x = 180
x = 36
So, x = 36 makes j||k.
7. Answer :
Because corresponding angles are congruent, the paths of the boats are parallel. Parallel lines do not intersect. So the paths of the boats will never cross.
8. Answer (i) :
m∠BEH = 58°
m∠DHG = 61°
∠BEH and ∠DHG are corresponding angles, but they are not congruent. So EB and HD are not parallel.
8. Answer (ii) :
m∠AEH = 62° + 58° = 120°
m∠CHG = 59° + 61° = 120°
∠AEH and ∠CHG are congruent corresponding angles. So AE and CH are parallel.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Oct 03, 23 12:34 AM
Oct 02, 23 11:40 PM
Oct 02, 23 08:32 PM