Prove the relation between side and diagonal in rhombus
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Answer:
To understand the relationship-between-a-rhombus-and-its-diagonals let us take a look at the properties of a rhombus which are as follows.
Rhombus. Its properties are
(a) All sides are equal.
(b) Opposite sides are parallel.
(c) Opposite angles are equal.
(d) Diagonals bisect each other at right angles.
(e) Diagonals bisect the angles.
(f) Any two adjacent angles add up to 180 degrees.
(g) The sum of the four exterior angles is 4 right angles.
(h) The sum of the four interior angles is 4 right angles.
(i) The two diagonals form four congruent right angled triangles.
(j) Join the mid-points of the sides in order and you get a rectangle.
(k) Join the mid-points of the half the diagonals in order and you get a rhombus.
(l) The distance of the point of intersection of the two diagonals to the mid point of the sides will be the radius of the circumscribing of each of the 4 right-angled triangles.
(m) The area of the rhombus is a product of the lengths of the 2 diagonals divided by 2.
(n) The lines joining the midpoints of the 4 sides in order, will form a rectangle whose length and width will be half that of the main diagonals. The area of this rectangle will be one-fourth that of the rhombus.
(o) If through the point of intersection of the two diagonals you draw lines parallel to the sides, you get 4 congruent rhombus each of whose area will be one-fourth that of the original rhombus.
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Answer:
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Step-by-step explanation:
The diagonals of a rhombus intersect at equal angles, while the diagonals of a rectangle are equal in length. The figure formed by joining the midpoints of the sides of a rhombus is a rectangle, and vice versa.
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