Question

AD and BC are equal and perpendicular to a
line segment AB show that.cD biseds AB
​

Answer 1

$\huge \mathsf{\orange {\underline {\purple {\underline { Required \ answer \ ♡ \ :- }}}}}$

$\bf{\underline{to\: a\: line\: segment\: AB. \:Show\: that\: }}$

$\bf{\underline{ CD\:bisects\: AB.}} </p><p>$

$\mathbb{ SOLUTION } :$

Given,

AD and BC are perpendiculars of AB.

$\mathbb{ TO \:BE \:SHOWN } :$

CD bisects AB

∠BOC = ∠DOC ( ∴ Vertically opposite angles )

DA = BC

∠B = ∠A = 90°

So, by $\bf{AAS} [tex] congruence condition, ΔBOC ≅ ΔOAD</p><p></p><p>So,</p><p>now CO = OD</p><p>so, it bisects AB on point '\bf{O}O '</p><p></p><p>OA = OB [ by CPCT ]</p><p></p><p>➖➖➖➖➖➖➖➖➖➖➖➖➖</p><p></p><p>[tex]\bf{AAS}$ : Angle-Angle-side

$\bf{CPCT}$ : Corresponding Parts of Congruent Triangles