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Ex.7.3 Q5 Triangles Solution - NCERT Maths Class 9

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\( ABC\) is an isosceles triangle with

\(AB = AC\). Draw \(AP ⊥ BC\) to show that \(\angle B = \angle C\).

 Video Solution
Ex 7.3 | Question 5

Text Solution

What is Known?

\(ABC\) is an isosceles triangle with \(AB \;\;AC\) and \(AP \;BC\)

To prove:

\[\angle \text{B}=\angle \text{C}\]


We can show triangles \(APB\) and \(APC\) congruent by using RHS congruency and then we can say corresponding parts of congruent triangles are equal to show the required result.


In \(\Delta APB\) and \(\Delta APC\),

\[\begin{align} \angle APB & = \angle APC\;(\text{Each }90^{\circ})\\  AB &= AC \;(\text {Given})\\  AP& = AP \;(\text {Common})\\  \Delta APB &\cong \Delta APC \\&(\text {Using RHS congruence rule})\end{align}\]

\[\angle B = \angle C\;(\text{By using }CPCT)\]

 Video Solution
Ex 7.3 | Question 5
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