Diagonals of rhombus ABCD intersect each other at point O. Prove that : OA 2 + OC 2 = 2AD 2 -

By formula, By pythagoras theorem, ⇒ (Hypotenuse) 2 = (Perpendicular) 2 + Base 2 In right angle triangle AOD, By pythagoras theorem, ⇒ AD 2 = OA 2 + OD 2 ⇒ OA 2 = AD 2 - OD 2 ..........(1) In right angle triangle COD, By pythagoras theorem, ⇒ CD 2 = OC 2 + OD 2 ⇒ OC 2 = CD 2 - OD 2 ..........(2) To prove : OA 2 + OC 2 = 2AD 2 - Solving L.H.S. of the above equation, we get : ⇒ OA 2 + OC 2 = AD 2 - OD 2 + CD 2 - OD 2 ⇒ OA 2 + OC 2 = AD 2 + CD 2 - 2OD 2 .........(3) Since, all sides of a rhombus are equal and diagonals of rhombus bisect each other, ∴ CD = AD and OD = Substituting value of CD and OD in equation (3), we get : ⇒ OA 2 + OC 2 = AD 2 + AD 2 - ⇒ OA 2 + OC 2 = 2AD 2 - ⇒ OA 2 + OC 2 = 2AD 2 - = R.H.S. Hence, proved that OA 2 + OC 2 = 2AD 2 - .

If a side of a rhombus is 10 cm and one of the diagonals is 16 cm, find the other diagonal.

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In the given figure, diagonals AC and BD intersect at right angle. Show that :
AB² + CD² = AD² + BC²

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In the figure, AB = BC and AD is perpendicular to CD. Prove that :
AC² = 2.BC.DC.

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In an isosceles triangle ABC; AB = AC and D is a point on BC produced. Prove that :
AD² = AC² + BD.CD

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Mathematics

Diagonals of rhombus ABCD intersect each other at point O. Prove that : OA<sup>2</sup> + OC<sup>2</sup> = 2AD<sup>2</sup> -

Pythagoras Theorem

Related Questions

If a side of a rhombus is 10 cm and one of the diagonals is 16 cm, find the other diagonal.

In the given figure, diagonals AC and BD intersect at right angle. Show that :
AB² + CD² = AD² + BC²

In the figure, AB = BC and AD is perpendicular to CD. Prove that :
AC² = 2.BC.DC.

In an isosceles triangle ABC; AB = AC and D is a point on BC produced. Prove that :
AD² = AC² + BD.CD

Mathematics

Diagonals of rhombus ABCD intersect each other at point O. Prove that : OA<sup>2</sup> + OC<sup>2</sup> = 2AD<sup>2</sup> -

Pythagoras Theorem

Related Questions

If a side of a rhombus is 10 cm and one of the diagonals is 16 cm, find the other diagonal.

In the given figure, diagonals AC and BD intersect at right angle. Show that :AB2 + CD2 = AD2 + BC2

In the figure, AB = BC and AD is perpendicular to CD. Prove that :AC2 = 2.BC.DC.

In an isosceles triangle ABC; AB = AC and D is a point on BC produced. Prove that :AD2 = AC2 + BD.CD

In the given figure, diagonals AC and BD intersect at right angle. Show that :
AB² + CD² = AD² + BC²

In the figure, AB = BC and AD is perpendicular to CD. Prove that :
AC² = 2.BC.DC.

In an isosceles triangle ABC; AB = AC and D is a point on BC produced. Prove that :
AD² = AC² + BD.CD