Parallel Lines in Cross Pattern: Identifying 6 Line Pairs with Right Angles

Parallel Lines with Cross-Pattern Recognition

Assuming all angles present are right angles, does the figure contain 6 pairs of parallel lines?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Are there 6 pairs of parallel lines?
00:03 All angles are right angles according to the given data
00:07 Corresponding angles between parallel lines sum to 180
00:12 All lines are parallel due to the corresponding angles
00:42 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Assuming all angles present are right angles, does the figure contain 6 pairs of parallel lines?

2

Step-by-step solution

Let's remember that parallel lines are two straight lines that lie in the same plane and never intersect (do not cross).

Let's draw all the right angles in the drawing, and extend the lines to create parallel lines, as follows:

We saw that we marked 8 right angles in the drawing, now let's mark each pair of parallel lines:

126435

Note that in the drawing we marked 6 pairs of parallel lines.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: Parallel lines never intersect and lie in same plane
  • Technique: Extend segments through right angles to form complete lines
  • Check: Count all line pairs that run in same direction ✓

Common Mistakes

Avoid these frequent errors
  • Counting line segments instead of complete parallel lines
    Don't count just the visible segments in the figure = you'll miss parallel pairs! Short segments can be part of longer parallel lines. Always extend segments through right angles to see the complete parallel lines.

Practice Quiz

Test your knowledge with interactive questions

What do the four figures below have in common?

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FAQ

Everything you need to know about this question

How do I know which lines are actually parallel?

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Parallel lines run in the same direction and never meet. In this cross pattern, look for lines that go horizontally (left-right) and vertically (up-down) - these form your parallel pairs.

Why do I need to extend the line segments?

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The figure only shows segments, but parallel lines are infinite! By extending through the right angles, you can see the complete lines and identify all parallel pairs.

What if some angles weren't right angles?

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Right angles guarantee that horizontal and vertical lines are perpendicular to each other. Without right angles, you'd need to measure angles or use other methods to identify parallel lines.

How do I systematically count parallel line pairs?

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First, identify all horizontal lines and count pairs. Then identify all vertical lines and count pairs. For this figure: 3 horizontal lines give 3 pairs, 3 vertical lines give 3 pairs, totaling 6 pairs.

Are the diagonal lines in the cross pattern parallel?

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No! In this figure, the lines only run horizontally and vertically. There are no diagonal lines, so you only need to consider horizontal and vertical parallel pairs.

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