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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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 _____ .

The correct option is B OD = OC Consider ΔBOC and ΔAOD 1) AD = BC ( Given ) 2) ∠CBO=∠DAO= 90° 3) ∠BOC=∠AOD ......(vertically opposite angles) ∴ΔBOC≅ΔAOD ....[AAS Criterion] ⇒ OC = OD ....(congruent parts of congruent triangle)