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 _____ .

$O D$ = $\frac{1}{2}$ $O C$

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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

Consider $Δ B O C$ and $Δ A O D$
1) AD = BC ( Given )
2) $∠ C B O = ∠ D A O$ = 90°
3) $∠ B O C = ∠ A O D$ ......(vertically opposite angles)

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

$\Rightarrow$ OC = OD ....(congruent parts of congruent triangle)

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Similar questions

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

A B

C D

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

O D = O C

A D ∥ B C

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.

A B

C D

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

O D = O C

△ A O D ≅ △ B O C

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