Three statements are given below:(I) In a ∆ABC in which AB=AC, the altitude AD bisects BC.(II) If the altitudes AD, BE and CF of ∆ABC are equal, then ∆ABC is equilateral.(III) If D is the midpoint ...

Question

Three statements are given below:(I) In a ∆ABC in which AB=AC, the altitude AD bisects BC.(II) If the altitudes AD, BE and CF of ∆ABC are equal, then ∆ABC is equilateral.(III) If D is the midpoint of the hypotenuse AC of a right ∆ABC, then BD=AC.Which is true?

Philoid · Accepted Answer

Here we can clearly see that the true statements are as follows:

(I) In a ∆ABC in which AB=AC, the altitude AD bisects BC.

(II) If the altitudes AD, BE and CF of ∆ABC are equal, then ∆ABC is equilateral.

∴ Option C is correct

Assertion (A)	Reason (R)
If AD is a median of ∆ABC, then AB+AC>2AD.	The angles opposite to equal sides of a triangle are equal.

Three statements are given below:
(I) In a ∆ABC in which AB=AC, the altitude AD bisects BC.

(II) If the altitudes AD, BE and CF of ∆ABC are equal, then ∆ABC is equilateral.

(III) If D is the midpoint of the hypotenuse AC of a right ∆ABC, then BD=AC.

Which is true?

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