Ex.7.3 Q4 Triangles Solution - NCERT Maths Class 9

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Question

\(BE\) and \(CF\) are two equal altitudes of a triangle \(ABC\). Using RHS congruence rule, prove that the triangle \(ABC\) is isosceles.

 Video Solution
Triangles
Ex 7.3 | Question 4

Text Solution

What is Known?

\(BE\) and \(CF\) are two equal altitudes of a triangle \(ABC.\)

To prove:

Triangle \(ABC\) is isosceles by using RHS congruence rule.

Reasoning:

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

Steps:

In \(\Delta BEC\) and \(\Delta CFB\),

\[\begin{align} \angle BEC & = \angle CFB\;(\text{Each }90^{\circ})\\  BC &= CB\;(\text{Common})\\  BE &= CF\;(\text{Given})\\ \therefore \Delta BEC  &\cong \Delta CFB\\ &\text{(By RHS congruency)} \end{align}\]

\(\therefore \angle BCE = \angle CBF (\text{By }CPCT)\)

\(\therefore AB = AC\) (Sides opposite to equal angles of a triangle are equal) Hence, \(\Delta ABC\) is isosceles.

  
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