How to prove that diagonals of a rhombus are not equal
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PROOF: A rhombus ABCD, AC & DB are diagonals.
In triangle DAB & triangle CAB
AD = BC ( opposite sides)
AB = AB ( common side)
And there are no other equal elements in these 2 triangles, for making the triangles congruent. Congruence criterion , which can be applied here is SAS .
SO, for applying SAS, <A = <B.
=> adjacent angles should be equal.
Since their sum = 180°
So, each angle = 90° ( if angles are equal)
In such case, Rhombus takes the shape of a Square.
And in this condition , triangles become congruent &
So, diagonals AC = BD ( corresponding parts of congruent triangles)
In triangle DAB & triangle CAB
AD = BC ( opposite sides)
AB = AB ( common side)
And there are no other equal elements in these 2 triangles, for making the triangles congruent. Congruence criterion , which can be applied here is SAS .
SO, for applying SAS, <A = <B.
=> adjacent angles should be equal.
Since their sum = 180°
So, each angle = 90° ( if angles are equal)
In such case, Rhombus takes the shape of a Square.
And in this condition , triangles become congruent &
So, diagonals AC = BD ( corresponding parts of congruent triangles)
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