In the figure given below, AD and BC are equal and perpendicular to the line segment AB. CD cuts AB at O. Then the relation between OC and OD is

OD = (1/2)OC

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OD =OC

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OD > OC

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OD < OC

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Solution

The correct option is B
OD =OC

Given that AD = BC,
$∠ C B O = ∠ D A O$ (both are right angles)
$∠ B O C = ∠ A O D$ (vertically opposite angles)

$∴$ $Δ B O C ≅ Δ A O D$ [AAS criterion]

Since corresponding sides of congruent triangles are equal,

OC = OD

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Similar questions

In the figure given below, AD and BC are equal and perpendicular to the same line segment AB. CD cuts AB at O. Then the relation between OC and OD is _____ .

Q. OA perpendicular to OD, OC perpendicular to OB, OD = OA, OC = OB. Then prove that AB = CD

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A B

and

C D

are intersecting at

^{'} O^{'}, O A = O B

and

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. Show that

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is equal to

Let AB and CD be two line segments such that AD and BC intersect at O. Suppose AO = OC and BO = OD. Prove that AB = CD.

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In the figure given below, AD and BC are equal and perpendicular to the line segment AB. CD cuts AB at O. Then the relation between OC and OD is

The correct option is B OD =OC Given that AD = BC, ∠CBO=∠DAO (both are right angles) ∠BOC=∠AOD (vertically opposite angles) ∴ ΔBOC≅ΔAOD [AAS criterion] Since corresponding sides of congruent triangles are equal, OC = OD

The correct option is B
OD =OC

Given that AD = BC,
$∠ C B O = ∠ D A O$ (both are right angles)
$∠ B O C = ∠ A O D$ (vertically opposite angles)

$∴$ $Δ B O C ≅ Δ A O D$ [AAS criterion]

Since corresponding sides of congruent triangles are equal,

OC = OD