**NCERT Class 10 Maths Lab Manual – Centroid of a Triangle**

**Objective**

To find the centroid of a triangle using paper cutting and foldinf activity

**Prerequisite Knowledge**

- Concept of finding the mid-point of a line segment by paper folding.
- Definition of medians.
- Meaning of Centroid.

**Materials Required**

Coloured papers, a pair of scissors, pencil, geometry box, fevistick.

**Procedure**

- Cut an acute angled triangle ABC from a coloured sheet of paper.

- Find the mid-points of sides AB, BC and AC by paper folding.

- Fold the triangle along AD, press it and unfold it, along BE, press it and unfold it, similarly fold the triangle along CF, fold it press it and unfold it.
- We get three creases AD, BE and CE These three creases are called medians and they meet or intersect or pass through one point say G.

- This point G is known as the centroid of a ∆ABC.

**Observation**

- We get three medians of ∆ABC as AD, BE and CF.
- The point of concurrence is known as the centroid of a ∆ABC.

**Result**

All three medians in a triangle intersect at a point called the centroid of the triangle.

**Learning Outcome**

Medians of an acute-angled triangle concurred at a point known as centroid, which always lies inside the triangle

**Activity Time**

Verify that the centroid of an obtuse-angled triangle and a right-angled triangle always lie inside the triangle.

**Viva Voce**

**Question 1.**

Define centroid.

**Answer:**

It is the point of concurrence of all three medians of a triangle.

**Question 2.**

Is the centroid lie outside the triangle ?

**Answer:**

No. It always lies inside the triangle.

**Question 3.**

In what ratio, the centroid divides the median from vertex to mid-point of the opposite side ?

**Answer:**

2:1

**Question 4.**

Define median.

**Answer:**

A line segment joining a vertex to the mid-point of its opposite side is known as a median.

**Question 5.**

Tell the number of medians in a triangle.

**Answer:**

3

**Question 6.**

In an equilateral triangle PQR, G is the centroid. What is the relationship between the areas of ∆GPQ, ∆GQR and ∆GPR?

**Answer:**

ar (∆GPQ) = ar(∆GQR) = ar(∆GPR)

**Question 7.**

Are three angle bisectors of a triangle meet at a point ?

**Answer:**

Yes (at incentre)

**Question 8.**

Is it correct to say that all three medians in a triangle are same in length ?

**Answer:**

No

**Multiple Choice Questions**

**Question 1.**

In a triangle, the centroid divides medians of the triangle in the ratio

(a) 1:2

(b) 2:1

(c) 2:3

(d) none of these

**Question 2.**

In a triangle ABC, if BD and AE are two medians which intersect at M. If BM = 6 cm, what is the value of BD ?

(d) 10 cm

(b) 2 cm

(c) 9 cm

(d) none of these

**Question 3.**

In a triangle EFG, if EP and FQ are two median intersecting at M such that MP = 8 cm, then the value of EM will be ‘

(a) 16 cm

(b) 4 cm

(c) 12 cm

(d) none of these

**Question 4.**

If PM and QR are two medians intersecting inside the ∆PQS at the point G, such that QG = 5 cm, then GR will be

(a) 2.5 cm

(b) 10 cm

(c) 4.5 cm

(d) none of these

**Question 5.**

In a right triangle PQS right angled at Q if PQ = 4 cm, QS = 6 cm, and PR and QT are two medians intersecting at G, what will be the value of PG?

(a) cm

(b) cm

(c) cm

(d) none of these

**Question 6.**

In an isosceles right-angled triangle ABC, if the length of each of the two equal sides is 6 cm, and the two medians AP and CQ intersect at M, the value of MQ will be

(a) √5 cm

(b) 2√5 cm

(c) 5√5 cm

(d) none of these

**Question 7.**

In an equilateral triangle ABC of side 6 cm, if two medians BP and CQ intersect each other inside the triangle at G, then the length of median will be

(a) 3√ 3cm

(b) different in length

(c) 5√3 cm

(d) none of these

**Question 8.**

In an isosceles triangle ABC, BD and CE are medians intersecting at M. If CE = 6 cm, what will be the value of other median BD ?

(a) 3 cm

(b) 6 cm

(c) 4 cm

(d) none of these

**Question 9.**

What will be the position of the centroid in an isosceles right-angled triangle ?

(d) inside

(b) outside

(c) on the triangle

(d) none of these

**Question 10.**

In an equilateral triangle, the lengths of three medians will be

(a) different

(b) can’t say

(c) same

(d) none of these

**Answers**

- (b)
- (c)
- (a)
- (a)
- (b)
- (a)
- (a)
- (b)
- (a)
- (b)

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