Rhombus Diagonal Length: Verify if DC = 8 cm in a 7 cm Side Rhombus

Rhombus Properties with Side Length Constraints

A rhombus has a side length measuring 7 cm.

Is DC equal to 8 cm?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Is the side D C equal to eight?
00:10 Remember, in a rhombus, all sides are the same length.
00:16 Let's substitute the side length based on the given information.
00:23 We'll find that D C actually equals seven, not eight.
00:32 And that's the solution to the question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

A rhombus has a side length measuring 7 cm.

Is DC equal to 8 cm?

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2

Step-by-step solution

Let's recall the properties of a rhombus. In a rhombus, all sides are equal to each other, therefore DC cannot be equal to 8 cm.

Additionally, in a rhombus, there are 2 pairs of parallel and equal sides. Since the side parallel to AB is CD, it must be equal to 7 cm.

3

Final Answer

No

Key Points to Remember

Essential concepts to master this topic
  • Rhombus Rule: All four sides are equal in length
  • Technique: Since AB = 7 cm, then DC = 7 cm
  • Check: Verify all sides equal: AB = BC = CD = DA = 7 cm ✓

Common Mistakes

Avoid these frequent errors
  • Confusing diagonal lengths with side lengths
    Don't assume DC = 8 cm just because it looks longer in the diagram = wrong comparison! Diagonals are different from sides and can be longer. Always remember that in a rhombus, all sides must be equal regardless of how the shape appears.

Practice Quiz

Test your knowledge with interactive questions

Look at the rhombus in the figure.

What is the relationship between the marked angles?

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FAQ

Everything you need to know about this question

Why can't DC be 8 cm if the side length is 7 cm?

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In a rhombus, all four sides must be equal. Since we're told the side length is 7 cm, every side including DC must also be 7 cm. This is a fundamental property of rhombuses.

What's the difference between sides and diagonals in a rhombus?

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Sides are the four edges of the rhombus (all equal), while diagonals are lines connecting opposite corners. Diagonals are usually different lengths and longer than the sides.

How can I tell which lines are sides in the diagram?

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The sides are the four edges forming the boundary: AB, BC, CD, and DA. These connect adjacent vertices. The number 7 shown in the diagram labels one of these sides.

Could DC be 8 cm in any quadrilateral?

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Yes! In rectangles, parallelograms, or irregular quadrilaterals, sides can have different lengths. But in a rhombus specifically, all sides must be equal.

What if the diagram makes DC look longer than 7 cm?

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Diagrams can be misleading due to perspective or scaling! Always rely on the given measurements and geometric properties rather than visual appearance.

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