Question

if P,Q,R are the mid point of three side AB,BC,CA respectively of an eqilateral triangle ABC prove that PQR in an eqilateral triangle​

Answer 1

Step-by-step explanation:

In the given figure, we have,

• ABC is an equilateral triangle.
• P, Q, R is the mid point of AB, BC and AC respectively.

To show:-PQR is an equilateral triangle.

Prove:-

In ∆ ABC,

P is the mid point of AB (given)

R is the mid point of AC (given)

so,

PR||BC

PR=1/2BC

Similarly,

P is the mid point of AB (given)

Q is the mid point of AB ( given)

so,

PQ||AC

PQ=1/2AC

Similarly,

Q is the mid point of BC ( given)

R is the mid point of AC (given)

so,

QR||AB

QR=1/2AB

Since, AB=BC=AC ( sides of equilateral triangle)

so,

1/2 AB=1/2 BC=1/2 AC

QR=PR=PQ (proved above)

Hence, PQR is an equilateral triangle.

PROVED.

HOPE IT HELPS