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 _____ .

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Solution

Consider $△ B O C$ and $△ A O D$
1) $A D = B C$ ( 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 _____ .

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

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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 _____ .

Consider △BOC and △AOD 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)

Consider $△ B O C$ and $△ A O D$
1) $A D = B C$ ( 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)