# Ex.7.3 Q5 Triangles Solution - NCERT Maths Class 9

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## Question

\( ABC\) is an isosceles triangle with

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

Video Solution

Triangles

Ex 7.3 | Question 5

## Text Solution

**What is Known?**

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

**To prove:**

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

**Reasoning:**

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.

**Steps:**

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

Triangles

Ex 7.3 | Question 5