Parallel Lines in a 5cm Square: Are AB and CD Parallel?

Parallel Line Properties with Square Geometry

A square has sides measuring 5 cm.

Is AB parallel to CD?

555AAABBBDDDCCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is AB parallel to CD?
00:03 ABCD is a square according to the given, therefore all angles are right angles
00:09 In a square, each pair of opposite sides is parallel
00:15 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

A square has sides measuring 5 cm.

Is AB parallel to CD?

555AAABBBDDDCCC

2

Step-by-step solution

Let's think about the different types of lines.

Looking at side AB and side CD, we can see that if we extend both of them, they will never intersect.

Also, according to the properties of a rectangle, each pair of opposite sides are parallel to each other.

Therefore, the answer is correct and indeed AB is parallel to CD.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Definition: Parallel lines never intersect, no matter how far extended
  • Property: In squares, opposite sides are always parallel by definition
  • Check: Extend lines AB and CD mentally - they never meet ✓

Common Mistakes

Avoid these frequent errors
  • Thinking adjacent sides are parallel
    Don't assume sides that share a corner (like AB and BC) are parallel = wrong answer! Adjacent sides in a square meet at 90° angles and intersect. Always identify opposite sides - AB is opposite to CD, not adjacent sides.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

Is a parallelogram a square?

FAQ

Everything you need to know about this question

How can I tell which sides are opposite in a square?

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Opposite sides don't share any vertices! In this square, AB (top) is opposite to CD (bottom), and AC (left) is opposite to BD (right). Adjacent sides share a corner.

Why are opposite sides of a square always parallel?

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By definition, a square has four right angles and equal sides. This geometric structure forces opposite sides to run in exactly the same direction, making them parallel.

What if the square was tilted or rotated?

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The orientation doesn't matter! Whether the square sits normally or is rotated, opposite sides remain parallel because the internal angles stay the same.

How is this different from other quadrilaterals?

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Not all quadrilaterals have parallel sides! Only parallelograms (including squares, rectangles, and rhombuses) guarantee that opposite sides are parallel.

Do I need to measure anything to determine if sides are parallel?

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No measurements needed! Since we're told it's a square, we automatically know opposite sides are parallel. The 5 cm measurement just tells us the size.

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