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Since the diagonals of a rhombus are perpendicular between them, then in one forth part of the rhombus they form a right triangle where hypotenuse is the side of the rhombus, the base and the height are one half part of its diagonals. Let's take a look at this right triangle.

The base and the height lengths could be congruent if and only if the angles opposite to them have a measure of 45⁰, which is impossible to a rhombus because these angles have different measures as they are one half of the two adjacent angles of the rhombus (the diagonals of a rhombus bisect the vertex angles from where they are drawn), which also have different measures (their sum is 180⁰ ).

Therefore, the diagonals of a rhombus are not congruent as their one half are not (the diagonals of a rhombus bisect each other).

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โˆ™ 2009-12-14 18:52:00
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Q: Prove that a rhombus has congruent diagonals?
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Related questions

Are the diagonals congruent in a rhombus?

The diagonals are perpendicular, but not necessarily congruent.


Are the diagonals of a rhombus congruent?

No, the diagonals of a rhombus are not congruent, but they do intersect each other at 90 degrees.


Do rhombus have congruent diagonals?

No


Are the diagonals of a rhombus always congruent?

No. The diagonals are perpendicular, but they dont have to be congruent.


Is the diagonals of rhombus congruent?

"Congruent" isn't used to describe the diagonals of a rhombus. However, all four sides of a rhombus are congruent - they are all the same length.The diagonals of a rhombus are perpendicular to each other. They are not the same length - if the diagonals were the same length, then you would have a square.


If a quadralateral has four congruent sides but its diagonals are not congruent it is a?

Rhombus


What quadrilateral has four congruent sides but its diagonals are not congruent?

Rhombus.


Are the diagonals congruent if a rhombus is a parallelogram?

No not normally only if the parallelogram is in the form of a rectangle will it then have congruent diagonals.


Are diagonals always congruent?

In a quadrilateral, the diagonals are only congruent for rectangles (or squares, which is a special kind of rectangle). Note: they are not congruent for a Rhombus.


Are the diagonals of a rhombus ever congruent?

Yes, if they are a square.


Is the diagonals of a rhombus always congruent?

Yes because a rhombus is like a parallelogram


What polygons always have congruent diagonals?

Regular polygons. A square and rectangle will have congruent (equal length) diagonals.

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