Analyzing Parallel Lines: Rectangle-Square Geometric Configuration

Parallel Line Properties with Rectangle Configurations

Two rectangles are drawn on the sides of a square.

Determine whether the opposite sides parallel in the diagram?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Are the opposite sides parallel in the drawing?
00:03 In a square and rectangle all angles are right angles
00:07 In a square and rectangle each pair of opposite sides are parallel
00:11 Any line parallel to another line
00:14 Must also be parallel to any line that is parallel to the line parallel to it
00:18 Therefore all opposite sides in the drawing are parallel
00:21 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Two rectangles are drawn on the sides of a square.

Determine whether the opposite sides parallel in the diagram?

2

Step-by-step solution

The two pairs of opposite sides are parallel because the two rectangles are connected to form a square, creating a 90-degree angle.

Therefore, the opposite sides in the drawing must be parallel.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Rule: Opposite sides of rectangles are always parallel by definition
  • Technique: Identify rectangle pairs - if ABCD is rectangle, then AB || CD
  • Check: Verify 90° angles at vertices confirm rectangle properties ✓

Common Mistakes

Avoid these frequent errors
  • Confusing adjacent sides with opposite sides
    Don't identify adjacent sides as parallel = wrong conclusion! Adjacent sides in rectangles meet at 90° angles and are perpendicular, not parallel. Always identify opposite sides across from each other.

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 can I tell which sides are opposite in this diagram?

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Opposite sides are the ones that don't share a vertex (corner). In a rectangle, if you pick any side, the side directly across from it (not touching it) is the opposite side.

Why are opposite sides of rectangles always parallel?

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By definition, a rectangle is a quadrilateral with four right angles. When opposite sides both meet the other two sides at 90°, they must be parallel to each other!

What if the rectangles weren't connected to a square?

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It wouldn't matter! Any rectangle has opposite sides that are parallel, regardless of how it's positioned or what it's connected to. This is a fundamental property of rectangles.

How do I identify all the parallel lines in this figure?

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Look at each rectangle separately. In the left rectangle, top and bottom sides are parallel. In the right rectangle, top and bottom sides are parallel. The vertical sides of each rectangle are also parallel to each other.

Does the square in the middle affect the parallel lines?

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No! The square just connects the rectangles. Each rectangle maintains its own parallel opposite sides regardless of what it's attached to. The square has its own parallel opposite sides too!

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