Square Geometry: Comparing Distances BE and CE from Diagonal Intersection

Square Diagonals with Equal Distance Properties

Look at the square below.

AAABBBDDDCCCEEE

Is BE equal to CE?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is BE equal to CE?
00:03 In a square, all sides are equal
00:08 In a square, the diagonals are angle bisectors
00:11 In a square, the diagonals are perpendicular to each other
00:14 In an isosceles triangle, the perpendicular is also a median
00:17 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

Look at the square below.

AAABBBDDDCCCEEE

Is BE equal to CE?

2

Step-by-step solution

According to the properties of the square, the diagonals intersect each other, therefore, BE is equal to CE

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Square Property: Diagonals bisect each other at the center point
  • Technique: Point E is the intersection creating equal segments BE and CE
  • Check: Both BE and CE are half the diagonal length ✓

Common Mistakes

Avoid these frequent errors
  • Confusing diagonal intersection with side measurements
    Don't measure from vertices to sides instead of to the center = wrong distances! This ignores that E is the diagonal intersection point. Always identify E as the center where diagonals cross, making all segments from E to vertices equal.

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

Why are BE and CE always equal in any square?

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In a square, the diagonals always bisect each other at right angles. This means point E divides both diagonals exactly in half, making all four segments from E to each vertex equal.

What if the square is tilted or rotated?

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The orientation doesn't matter! A square's properties remain the same regardless of how it's positioned. The diagonals still bisect each other equally.

How is this different from a rectangle?

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In rectangles, diagonals bisect each other too, but they're not equal length. In squares, diagonals are both equal length AND bisect each other, making segments like BE and CE always equal.

Can I use this property to solve other problems?

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Yes! This diagonal property helps with distance calculations, finding coordinates, and proving geometric relationships in squares and other problems involving square geometry.

What about other diagonal segments like AE and DE?

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All four segments from the center E to each vertex are equal! So AE = BE = CE = DE. This is because E is equidistant from all four corners of the square.

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