Question

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal.

refer to the attachment

please solve it​

Answer 1

Answer:

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□Given :-

• ABC is an issoceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively.

□To prove :-

• The altitudes BE and CF are equal.

□Explanation :-

• Here you refer the attachment for more information and for getting better answer .
• In attachment i answered your question.

Used formula :-

• By ASA congruency here we find the answer.

For more information :-

• https://Brainly.in/question/5714440.
• https://Brainly.in/question/24152394
• search on web.

□Hope it helps u mate .

□Thank you .

Answer 2

Given :-

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB.

To Show :-

• Altitude BE = CF

Solution :-

• To show BE = CF at first we have to assume something on the basis of the question. As given in the question that AB = AC. Note if two sides of triangle are equal then it is said to be isoceles triangle. To show BE = CF , here we have to prove congruency as per the triangle Congruency property.

Let's focus on BEC abd BFC :-

⟹ In right angle triangle BEC and BFC

⟹ BC = BC (common side)

⟹ ∠BFC = ∠BEC (each 90°)

⟹ BF = EC (AB = AC)

∴ ∆ BEC ≅ ∆ BFC (By S.A.S criteria of congruency)

∴ BE = CF (By CPCTC)

Hence , proved BE = CF