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# Prove that a rhombus has congruent diagonals?

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). Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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