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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 45â°, 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 180â° ).
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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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.
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.
What polygons always have congruent diagonals?
Regular polygons. A square and rectangle will have congruent (equal length) diagonals.
Are the diagonals of a rhombus ever congruent?
Yes, if they are a square.
Which quadrilateral must have diagonals that are congruent and perpendicular?
The quadrilateral that must have diagonals that are congruent and perpendicular is the square. This is because its diagonals form a right angle at its center.
