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Ex.7.1 Q3 Triangles Solution - NCERT Maths Class 9

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\(AD\) and \(BC\) are equal perpendiculars to a line segment \(AB\) (See the given figure). Show that \(CD\) bisects \(AB\).

 Video Solution
Ex 7.1 | Question 3

Text Solution

What is Known?

\({\text{AD}} \bot {\text{AB, BC}} \bot {\text{AB}}\;{\text{and AD}} = {\text{BC}}\)

To prove:

\(CD\) bisects \(AB\) or \(OA = OB\)


We can show two triangles \(OBC\) and \(OAD\) congruent by using AAS congruency rule and then we can say corresponding parts of congruent triangles will be equal.


In \(\Delta BOC\) and \(\Delta AOD\),

\[\begin{align}\angle BOC& = \angle AOD\\\text{(Vertically opp}&\text{osite angles)}\\\\\angle CBO &= \angle DAO\text{(Each}\, 90^ {\circ})\\BC &= AD \text{(Given)}\\\therefore \Delta BOC &\cong \Delta AOD\\ \text{(AAS} \,& \text{congruence rule)}\\\\\therefore BO &= AO \text{(By CPCT)}\end{align}\]

Hence \(CD\) bisects \(AB\).

 Video Solution
Ex 7.1 | Question 3
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