Identify Parallel Sides in ABCD Rectangle: Geometric Analysis

Q: How do I tell which sides are opposite in a rectangle?

Opposite sides don't share any vertices! In rectangle ABCD: AB (top) is opposite DC (bottom), and BC (right) is opposite AD (left). Think of them as across from each other.

Q: Are adjacent sides ever parallel in a rectangle?

Never! Adjacent sides (like AB and BC) meet at corners and form right angles. They are perpendicular, which means they're at 90° to each other, not parallel.

Q: Do I need to measure the sides to know they're parallel?

No! If you can see it's a rectangle from the right angle markers in the corners, you automatically know opposite sides are parallel. It's a defining property of rectangles.

Rectangle Properties with Parallel Side Identification

Which sides are parallel to each other?

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Step-by-step video solution

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00:00 Find the parallel lines

00:05 If corresponding angles are supplementary to 180° - then the lines are parallel

00:35 And this is the solution to the question

Step-by-step written solution

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Understand the problem

Which sides are parallel to each other?

Step-by-step solution

To solve this problem, we'll examine the provided figure to determine which sides are parallel.

Based on the diagram:

The side $AB$ is opposite side $DC$ , and they are aligned horizontally and parallel to each other.
Similarly, the side $BC$ is opposite side $AD$ , and they are aligned vertically and parallel to each other.

This analysis indicates that the quadrilateral depicted is a rectangle, where opposite sides are parallel.

Therefore, the parallel sides are $AB \parallel DC$ and $BC \parallel AD$ .

This confirms the correct choice from the options given.

Therefore, the solution to the problem is $AB||DC$ and $BC||AD$ .

Final Answer

AB||DC and BC||AD

Key Points to Remember

Essential concepts to master this topic

Rectangle Rule: Opposite sides are always parallel and equal in length
Technique: Identify opposite sides: AB is opposite DC, BC is opposite AD
Check: Verify both pairs: $AB \parallel DC$ and $BC \parallel AD$ ✓

Common Mistakes

Avoid these frequent errors

Confusing adjacent sides as parallel
Don't say AB||BC or adjacent sides are parallel = wrong answer! Adjacent sides in rectangles meet at right angles and are perpendicular, not parallel. Always identify opposite sides: AB opposite DC, BC opposite AD.

Practice Quiz

Test your knowledge with interactive questions

The lines below are not the same size, but are they parallel?

FAQ

Everything you need to know about this question

How do I tell which sides are opposite in a rectangle?

Opposite sides don't share any vertices! In rectangle ABCD: AB (top) is opposite DC (bottom), and BC (right) is opposite AD (left). Think of them as across from each other.

Are adjacent sides ever parallel in a rectangle?

Never! Adjacent sides (like AB and BC) meet at corners and form right angles. They are perpendicular, which means they're at 90° to each other, not parallel.

What's the difference between || and ⊥ symbols?

The symbol || means parallel (never meet), while ⊥ means perpendicular (meet at 90°). In rectangles: opposite sides are || and adjacent sides are ⊥.

Do I need to measure the sides to know they're parallel?

No! If you can see it's a rectangle from the right angle markers in the corners, you automatically know opposite sides are parallel. It's a defining property of rectangles.

What if the rectangle is tilted or rotated?

The parallel relationships stay the same! Even if the rectangle is rotated, opposite sides remain parallel to each other. The orientation doesn't change the geometric properties.

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