2 Lines Are Parallel If

In Geometry, a line is defined as a i-dimensional geometric figure that extends infinitely in both directions. A line has no thickness. A line is generally fabricated upwards of an infinite number of points. In this commodity, we will discuss the lines parallel to the aforementioned line and the theorem related to information technology with many solved examples.

Table of Contents:

What is Meant past Lines Parallel to the Aforementioned Line?
Solved Examples
Practise Problems
FAQs

What is Meant past Lines Parallel to the Same Line?

Theorem: Lines that are parallel to the same line are parallel to each other.

It means that if ii lines are parallel to the same line, and so they will be parallel to each other. Now, allow u.s.a. bank check this theorem with the help of the below figure.

Lines Parallel to the Same Line

From the given effigy, nosotros tin can say that line m is parallel to line l and line n is parallel to line l. (i.e) line m || line 50 and line n || line l. Also, "t" is the transversal for the lines l, g and n.

Therefore, we tin can say that ∠ane = ∠2 and ∠one = ∠3. (Past corresponding angles axioms).

So, nosotros can as well say that ∠two and ∠3 are corresponding and they are equal to each other.

Thus, ∠2 = ∠three

Past using the converse of corresponding angle axioms, we conclude that line m is parallel to line n.

(i.east) Line m || Line n.

Notation: This property tin be extended to more than two lines also.

Solved Example

Example:

From the given figure, AB is parallel to CD and CD is parallel to EF.

Lines Parallel to the Same Line -1

Also, given that EA is perpendicular to AB. Find the values of ten, y and z, if ∠BEF = 55°.

Solution:

Given that AB|| CD, CD || EF, EA ⊥ AB, and ∠BEF = 55°.

Therefore, y+ 55° = 180° (Interior angles on the same side of transversal ED)

Hence, y = 180°-55°= 125°

By using the corresponding angles axiom, AB || CD, we can say that ten = y.

Therefore, the value of x= 125°.

Since, AB || CD and CD || EF, therefore AB || EF.

And then, we tin write: ∠ FEA + ∠ EAB = 180° (Interior angles on the same side of transversal EA)

55° + z + xc° = 180°

z = 180° – ninety° – 55°

z = 180° – 145°

z = 35°

Therefore, the values of x, y and z are 125°, 125° and 35°, respectively.

Practice Problems

Solve the following problems:

one. From the given figure, AB ||CD and CD || EF and y:z = 3:7. Detect the value of 10.

Lines Parallel to the Same Line -2

2. From the given figure, if PQ || RS and ∠MXQ = 135° and ∠MYR = 40°, so detect the value of ∠XMY.

Lines Parallel to the Same Line -3

Stay tuned with BYJU'S – The Learning App and acquire more class-wise concepts easily past exploring more videos.

Frequently Asked Questions on Line Parallel to the Aforementioned Line

What is meant by a line parallel to the aforementioned line?

The lines which are parallel to the aforementioned line are parallel to each other.

Which symbol is used to stand for the parallel line?

The symbol used to correspond the parallel line is "||".

What is meant by parallel lines?

The parallel lines are the lines that are equidistant from each other and they never intersect each other.

Mention 3 properties of angles associated with parallel lines.

The respective angles are equal
Alternate interior angles are equal
Alternate outside angles are equal.

How practise you prove that the given lines are parallel lines?

To prove that the given lines are parallel, then nosotros have to evidence either corresponding angles are equal or alternate angles are equal or co-interior angles are supplementary.