Parallel lines They are lines whose distance between then does - PowerPoint PPT Presentation

D AY 4 – P ARALLEL LINES

I NTRODUCTION We see electric cables hanging between poles, athletic track lines and so many other similar features. Have we ever asked ourselves about a special feature about the lines that are identified with these situations? We meet lines that are separated from another by the same distance all along their length. This is of a great interest as far as this lessons is concerned. We are going to discuss, briefly, what these lines are.

V OCABULARY  Line This is a connection of so many points that extends continuous in both directions. By saying a line, in the presentation, we will be referring to a straight line.  Parallel lines These is a collection of two or more lines whose distance between them does not change.

 Parallel lines They are lines whose distance between then does not change along their length. In such situations, the do not meet. The diagram below shows three sets of lines where, in each set, the lines are parallel to one another.

When we say distance between parallel lines, we mean that the shortest distance between them is the same. This shortest distance is represented by line segments that are equal and perpendicular to the pairs of parallel lines. C M B H L F G D E A

In the figure above, 𝐵𝐶 and 𝐸𝐷 are parallel lines while 𝐺𝐹 = 𝐼𝐻 = 𝑁𝑀 are equal perpendicular lines (small marks on the lines implies that they are equal) that shows the equal distance along the length of the lines (parallel line). Parallel lines are denoted by two parallel short lines, ∥ . Thus, we write 𝐵𝐶 ∥ 𝐸𝐷 to mean 𝐵𝐶 is parallel to 𝐸𝐷 .

Sometimes, parallel lines are drawn with extra arrow(s) to show that they are parallel. L1 L2 L3 In the figure above, 𝑀4 and 𝑀5 are parallel and have L4 L5 two arrows showing that they are parallel to each other and not the other lines that have one arrow. Likewise, 𝑀1, 𝑀2 and 𝑀3 are parallel to each other.

Example1 Identify parallel lines among in the following figure. L 6 L 7 L 4 L 3 L 8 L 1 L 5 L 2

The parallel lines cannot meet and have an equal distance along their length. Based on this concept, we have that. 𝑀 1 ∥ 𝑀 2 ∥ 𝑀 5 ; 𝑀 6 ∥ 𝑀 7 and 𝑀 3 ∥ 𝑀 4 ∥ 𝑀 8

HOMEWORK Draw lines 𝑀 𝑛 and 𝑀 𝑜 given that 𝑀 𝑛 ∥ 𝑀 𝑜 .

A NSWERS TO HOMEWORK The lines must not meet and they should have an equal distance along their length.

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