Question

ad and bc are equal perpendiculars to a line segment AB. Which congruency rule is applicable to prove CD bisects AB. ​

Answer 1

Given :-

• AD and BC are equal perpendicular to AB

To prove :-

• CD bisects AB

Proof / Explanation :-

In ΔAOD and ΔBOC,

$\implies{ \angle \: A = \angle \: B} \: \: \: \: ( {90}^{ \circ} \: Each)$

${\implies{ \angle \: AOD = \angle \: BOC} \: \: (V.O.A)}$

$\implies{ AD = BC} \: \: \: \: (Given)$

Hence, ΔAOD ≅ ΔBOC by AAS congruence rule.

$\normalsize{\implies{ { \bf{AO = OB \: (CPCT)}}}}$

$\underline{ \boxed{\implies{ \therefore{CD \: bisect \: AB}}}}$

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NOTE :-

• V.O.A - Vertically Opposite Angles
• C.P.C.T - Corresponding parts of congruent triangles

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@Agamsain❤