The point of concurrency of the medians of a triangle is called the centroid of the triangle and is usually denoted by G.

**Construction of the Centroid of a Triangle**

**Centroid**

The point
of concurrency of the medians of a triangle is called the centroid of the triangle
and is usually denoted by *G*.

**Activity 8**

**Objective** To find the mid-point of a line segment
using paper folding

**Procedure** Make a line segment on a paper by folding
it and name it *PQ*. Fold the line segment *PQ* in such a way that *P*
falls on *Q* and mark the point of intersection of the line segment and the
crease formed by folding the paper as *M*. *M* is the midpoint of *PQ*.

**Example 4.12**

Construct
the centroid of Δ*PQR* whose
sides are *PQ* = 8cm; *QR* =
6cm; *RP* =
7cm.

*Solution*

**Step 1 **: Draw Δ*PQR* using
the given measurements *PQ* = 8cm *QR *= 6cm and* RP *=
7cm and construct the perpendicular bisector of any two sides (*PQ *and *QR*)
to find the mid-points *M *and* N *of* PQ *and* QR *respectively.

**Step 2 **: Draw the medians** ***PN***
**and *RM *and let them meet at* G*. The point *G* is the centroid
of the given Δ*PQR* .

**Note**

• Three medians can be drawn in a triangle

• The centroid divides each median in the ratio 2:1 from the vertex.

• The centroid of any triangle always lie inside the triangle.

• Centroid is often described as the triangle’s centre of gravity
(where the triangle balances evenly) and also as the barycentre.

Tags : Example Solved Problems | Practical Geometry , 9th Maths : UNIT 4 : Geometry

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9th Maths : UNIT 4 : Geometry : Construction of the Centroid of a Triangle | Example Solved Problems | Practical Geometry

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