Ex.7.2 Q7 Triangles Solution - NCERT Maths Class 9

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Question

\(ABC\) is a right-angled triangle in which

\(\angle A = 90^{\circ}\) and \(AB = AC\). Find \(\angle B\) and \(\angle C\).

 Video Solution
Triangles
Ex 7.2 | Question 7

Text Solution

What is Known?

\(ABC \) is right-angled triangle and sides \(AB=AC\)

To Find:

Value of \(∠B\) and \(∠C.\)

Reasoning:

We can use the property angles opposite to equal sides are equal and then by the angle sum property in triangle \(ABC \) we can find the value of \(∠B\) and \(∠C.\)

Steps:

It is given that

\[\begin{align} &\quad\, AB=AC\\ &\therefore \angle C=\angle B \\  & \left( \begin{array}{I}   \text{Angles opposite  to equal sides } \\   \text{of a  triangle are also equal}\text{.} \\ 
\end{array} \right) \\ \end{align}\]

In \(\Delta ABC,\)  

\[\begin{align} \angle A+\angle B+\angle C&=180^{\circ}\\ (\text{Angle sum property}&\text{ of a triangle}) \\\\ 90^{\circ}+\angle B+\angle C&=180^{\circ} \\ 90^{\circ}+\angle B+\angle B&= 180^{\circ} \\ 2\angle B&= 90^{\circ} \\ \angle B&=45^{\circ} \\ \therefore \angle B=\angle C&=45^{\circ} \\ \end{align}\]

 Video Solution
Triangles
Ex 7.2 | Question 7
  
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