Question

construct an equilateral triangle PQR with each side of 7cm , Also construct perpendicular bisect of each side. And write your observation for perpendicular bisector​

Answer 1

Answer:

Steps for construction:

I) Construction of triangle

1) Let the base of the triangle be QR=8cm.

2) Taking Q as the centre and radius 4cm on the compass, draw and arc on the upper side of QR.

3) Taking R as the centre and radius 6cm on the compass, draw and arc on the upper side of QR, intersecting the previous arc. Mark this point of intersection as point P.

4) Join points P to Q and P to Q to complete the △PQR.

II) Construction of perpendicular bisectors

1) Taking Q as the centre and radius more than half of QR, mark arcs below and above the line.

2) Now, with R as the centre and same radius, draw arcs above and below the line to intersect the already drawn arcs. Name the new points as X and Y.

3) Join points X and Y. This line XY is the required perpendicular bisector of side QR.

4) Similarly, draw perpendicular bisectors of sides PQ and PR.

III) Construction of circumcircle

1) All the perpendicular bisectors of △PQR will intersect at one point in the interior of the triangle.

Name that point as O.

2) Taking point O as the centre and OP as the radius draw a circle. Points Q and R should also lie on this circle.

3) This is the required circumcircle.