Rectangle Verification: Analyzing Quadrilateral ABCD Using Diagonal Properties

Rectangle Properties with Diagonal Analysis

Look at the quadrilateral below.

Determine if the quadrilateral is a rectangle.

AAABBBCCCDDDEEE

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Step-by-step written solution

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1

Understand the problem

Look at the quadrilateral below.

Determine if the quadrilateral is a rectangle.

AAABBBCCCDDDEEE

2

Step-by-step solution

From the given information, we know that triangle EBC is equilateral.

In an equilateral triangle, all angles are equal to each other.

Therefore, angle B is equal to 60 degrees.

Since none of the angles are 90 degrees, we can safely say that the quadrilateral is not a rectangle.

3

Final Answer

It is not a rectangle.

Key Points to Remember

Essential concepts to master this topic
  • Rectangle Rule: All four angles must be exactly 90 degrees
  • Technique: Check if diagonals bisect each other and are equal length
  • Check: If any angle ≠ 90°, then not a rectangle ✓

Common Mistakes

Avoid these frequent errors
  • Assuming quadrilateral with equal diagonals is always a rectangle
    Don't just check diagonal properties without verifying angles = wrong classification! Equal diagonals don't guarantee 90° angles. Always verify that all four interior angles are exactly 90 degrees first.

Practice Quiz

Test your knowledge with interactive questions

True or false?

One of the angles in a rectangle may be an acute angle.

FAQ

Everything you need to know about this question

How can I tell if this quadrilateral is a rectangle just by looking at it?

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Look for right angles at each corner! In this diagram, the angles clearly aren't 90°. The quadrilateral appears slanted, which means it's a parallelogram but not a rectangle.

What does the point E tell us about this shape?

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Point E shows that triangle EBC is equilateral, meaning all its angles are 60°. Since angle B = 60° (not 90°), the quadrilateral cannot be a rectangle.

Can a shape have equal diagonals but not be a rectangle?

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Yes! Isosceles trapezoids have equal diagonals but aren't rectangles. Only rectangles have both equal diagonals and four 90° angles.

What makes this quadrilateral special if it's not a rectangle?

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This appears to be a parallelogram - opposite sides are parallel and equal. It has the diagonal properties shown, but lacks the 90° angles needed for a rectangle.

How do I remember what makes a rectangle different from other quadrilaterals?

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Remember: Rectangle = Four Right Angles! All rectangles are parallelograms, but not all parallelograms are rectangles. The key difference is those 90° corners.

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