Question

In a equilateral ∆ ABC , P , Q ,R are the midpoints of AB, BC , CA . Prove that PQR IS EQUILATERAL

Answer 1

Heya..

If ABC is an equilateral triangle and P, Q, R are mid points of these sides.

To prove :

PQR is an equilateral triangle.

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P is a mid point of AB and

R is a mid point of AC.

Hence PR = 1/2 BC (By Mid point Theorem)...... Eq. 1.

P is a mid point of AB and

Q is a mid point of BC.

Hence PQ = 1/2 AC (By Mid point Theorem)........ Eq. 2.

Q is a mid point of BC and

R is a mid point of AC.

Hence QR = 1/2 AB (By Mid point Theorem)........ Eq. 3.

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Compare eq 1,2 and 3..

As AB = BC = AC

(ABC is an equilateral triangle)

=) AB/2 = BC/2 = AC/2

=) QR = PR = PQ

=) PQR is an equilateral triangle.

Hope it's helpful to u.