Investigating Perpendicular Diagonals in a Rhombus: Geometric Analysis

Rhombus Properties with Diagonal Relationships

Look at the following rhombus:

Are the diagonals of the rhombus perpendicular to each other?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the following rhombus:

Are the diagonals of the rhombus perpendicular to each other?

2

Step-by-step solution

The diagonals of the rhombus are indeed perpendicular to each other (property of a rhombus)

Therefore, the correct answer is answer A.

3

Final Answer

Yes.

Key Points to Remember

Essential concepts to master this topic
  • Property: All rhombus diagonals are always perpendicular to each other
  • Recognition: Look for 90° angle markers where diagonals intersect
  • Verification: Check if diagonal intersection forms four right angles ✓

Common Mistakes

Avoid these frequent errors
  • Confusing rhombus with rectangle diagonal properties
    Don't assume rhombus diagonals are equal like rectangles = wrong geometric reasoning! Rectangle diagonals are equal but not always perpendicular, while rhombus diagonals are perpendicular but not always equal. Always remember that rhombus diagonals intersect at 90° angles.

Practice Quiz

Test your knowledge with interactive questions

Look at the following rhombus:

Are the diagonals of the rhombus parallel?

FAQ

Everything you need to know about this question

How can I tell if diagonals are perpendicular just by looking?

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Look for right angle markers (small squares) where the diagonals cross! In the diagram, you can see the diagonals form four equal angles at their intersection point.

Are rhombus diagonals always the same length?

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No! Rhombus diagonals are perpendicular but not necessarily equal in length. Only in a special rhombus called a square are the diagonals both perpendicular AND equal.

What makes a rhombus different from other quadrilaterals?

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A rhombus has all four sides equal and diagonals that are perpendicular. This is different from rectangles (equal diagonals) or parallelograms (no special diagonal properties).

Do the diagonals bisect each other in a rhombus?

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Yes! Rhombus diagonals not only cross at 90° angles but also bisect each other - meaning they cut each other exactly in half at the intersection point.

How do I prove diagonals are perpendicular?

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You can prove it by showing that the four angles formed where diagonals intersect are all 90° 90° . Since these angles are vertical angles, if one is 90°, all four are 90°!

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