Question

What are the line segments XA, YB and ZC called? Let these three line segments meet
at P. What will P be called?
7. If AD, BE and CF are the three medians intersecting at G. Measure AG and GD. Find a
relation between AG and GD.
8. In a right angled triangle PQR, ZPRQ = 90°. Draw the perpendicular bisectors of PR and
QR. Where do they meet?
[HOT]
9. The perpendicular bisectors of the sides of a triangle MNP intersect each other at 0. Join
OM, ON and OP. Is OM ON = OP?
9. In a right angled triangle ABC, AB is the hypotenuse. Which angle measures 90°?
Draw the right bisector (perpendicular bisector) of AB. Does it pass through C, when
AC = BC?
Fill in the blanks:
(i) The point of concurrence of the altitudes of a triangle is called
is the point where the angle bisectors of a triangle meet.
(iii) The
of a triangle are concurrent at the centroid.
(iv) The
is the point, where the perpendicular bisectors of the sides me
each other.​

Answer 1

Answer:

MATHS

From a point within a triangle, line segments are drawn to the vertices. A necessary and sufficient condition that the three triangles thus formed have equal areas is that the point be:

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ANSWER

To divide a triangle into three triangles of equal area is to find the centroid (the point where the medians intersect). After determining the centroid (point G below), construct the segments connecting the vertices to the centroid. The three triangle created are of equal area.

So from a point within a triangle, line segments are drawn to the vertices. A necessary and sufficient condition that the three triangles thus formed have equal areas is that the point be the intersection of the medians of the triangle