Square Diagonal Problem: Comparing BD and AC Distances in a 4 cm Square

Square Diagonals with Distance Properties

A square has side lengths

equal to 4 cm.

Is the distance between BD and AC equal to the length of BD?

444AAABBBDDDCCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Is CD equal to BD?
00:03 In a square all angles are right angles
00:14 The distance between AC and BD is side CD
00:19 In a square all sides are equal
00:28 Let's substitute the side length according to the given data
00:35 Since all sides are equal, CD equals BD
00:44 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 side lengths

equal to 4 cm.

Is the distance between BD and AC equal to the length of BD?

444AAABBBDDDCCC

2

Step-by-step solution

Firstly, let's think about the properties of a square—remembering that all sides are equal to each other.

In other words, all sides in the square are equal to 4 cm. As a result, we can determine that the distance between BD and AC is indeed equal to 4 since CD is also equal to 4.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Rule: Square diagonals are perpendicular and bisect each other at center
  • Technique: Distance between diagonals equals side length = 4 cm
  • Check: Diagonal length 42 4\sqrt{2} ≠ distance between diagonals 4 cm ✓

Common Mistakes

Avoid these frequent errors
  • Confusing diagonal length with distance between diagonals
    Don't calculate diagonal length 42 4\sqrt{2} = 5.66 cm when asked for distance between diagonals! The diagonal length uses Pythagorean theorem but distance between diagonals is different. Always identify what distance is being asked: diagonal length or perpendicular distance between diagonal lines.

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

What exactly is the 'distance between BD and AC'?

+

The distance between diagonals BD and AC is the perpendicular distance between these two lines. Think of it as the shortest distance from one diagonal to the other, measured at a right angle.

How is this different from the length of diagonal BD?

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The length of diagonal BD is how long the diagonal line is: 42 4\sqrt{2} ≈ 5.66 cm. The distance between diagonals is how far apart the two diagonal lines are: 4 cm.

Why does the distance between diagonals equal the side length?

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In a square, the diagonals are perpendicular and meet at the center. The distance between them equals the side length because of the square's symmetry properties.

Do I need to use the Pythagorean theorem here?

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No! The Pythagorean theorem gives you diagonal length, but this question asks for distance between diagonals. These are completely different measurements.

Is the answer always the same for any square?

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Yes! For any square, the distance between diagonals always equals the side length. This is a special property that makes squares unique among rectangles.

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