# Then The Triangle will be : If

Answered

If the median drawn on the base of a triangle is half its base, then the triangle will be

- obtuse angled
- equilateral
- right angled
- acute angled

Best answer

Answer: (3) Right angled triangle

Explanation:-

Let PQR be the triangle PO be the median.Then, PO = QR/2

By Apollonius theorem,

(PQ)^{2} + (PR)^{2} = 2 (PO^{2} + OQ^{2})

PO = OQ = OR = QR/2

Therefore, PQ^{2} + PR^{2} = 2[(QR/2)^{2} + (QR/2)^{2}]

PQ^{2} + PR^{2} = 2(QR^{2}/4 + QR^{2}/4)

PQ^{2} + PR^{2} = 2(QR^{2}/2)^{
}PQ^{2} + PR^{2} = QR^{2}

It follows Pythagoras theorem.

Hence, it is a right angled triangle.