P, Q and R are the mid-points of the sides of an equilateral triangle XYZ. Then PQR is

an equilateral triangle Reason Given, XYZ is an equilateral triangle. ⇒ XY = YZ = ZX P, Q and R are the mid-points of the sides of an equilateral triangle XYZ. By mid-point theorem, The line joining mid-point of any two sides of a triangle is parallel and is equal to half of third side. Since, P and Q are mid-points of sides XY and XZ, ∴ PQ || YZ and PQ = YZ (As we know, XY = YZ = ZX) ⇒ PQ = XZ ...................(1) And, Q and R are mid-points of sides XZ and YZ, ∴ QR || XY and QR = XY (As we know, XY = YZ = ZX) ⇒ QR = ...................(2) Similarly, P and R are mid-points of sides XY and YZ, ∴ PR || XZ and PR = XZ (As we know, XY = YZ = ZX) ⇒ PR = YZ ...................(3) From equation (1), (2) and (3), we can clearly say that ⇒ PQ = QR = PR = YZ ⇒ PQ = QR = PR Hence, PQR is also an equilateral triangle.

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In △ABC, AB = AC. D, E and F are mid-points of the sides BC, CA and AB respectively. Show that :
(i) AD is perpendicular to FE.
(ii) AD and FE bisect each other.

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Mathematics

P, Q and R are the mid-points of the sides of an equilateral triangle XYZ. Then PQR is

Mid-point Theorem

Related Questions

In △ABC, AB = AC. D, E and F are mid-points of the sides BC, CA and AB respectively. Show that :
(i) AD is perpendicular to FE.
(ii) AD and FE bisect each other.

Mathematics

P, Q and R are the mid-points of the sides of an equilateral triangle XYZ. Then PQR is

Mid-point Theorem

Related Questions

In △ABC, AB = AC. D, E and F are mid-points of the sides BC, CA and AB respectively. Show that :(i) AD is perpendicular to FE.(ii) AD and FE bisect each other.

In △ABC, AB = AC. D, E and F are mid-points of the sides BC, CA and AB respectively. Show that :
(i) AD is perpendicular to FE.
(ii) AD and FE bisect each other.