The Property of the Centroid of a Triangle

Q. AD, BE and CF are the medians of the triangle ABC and G is centroid. If $AD=15cm$, find $AG$.

1. 10

Q. The centroid of a triangle is located 12 units from one of the vertices of a triangle. Find the length of the median of the triangle drawn from that same vertex.

1. 18

Q. We can draw a triangle ABC in which BC is 12cm, $\angle B$ is ${75}^{\circ }$ and AB + AC = 6.5 cm.

1. True
2. False
3. Data insufficient
4. Cannot be determined

Q. The ratio in which the Centroid of the triangle divides the median is

1. 1 : 1
2. 3 : 1
3. 2 : 1
4. 3 : 2

Q. (a) For any triangle ABC, draw: [4 MARKS]
(i) All possible medians.
(ii) All possible altitudes.

(b) Find the unknown angles x and y.

Q. To divide a line segment of 12 cm into 8cm and 4cm, we have to mark number of points.

1. 12
2. 3
3. 6
4. 9

Q.

In the given figure, ∠ABC = ${90}^{\circ }$ and BM is a median, AB = 8 cm and BC = 6 cm. Then, length BM is equal to___________.

1. 3 cm

2. 4 cm

3. 5 cm

4. 7 cm

Q. In an equilateral triangle of side 6 cm each median is drawn from a vertex of the triangle to its opposite side, find the length of the altitude.

Q. In what ratio does the centroid divide each median?

1. 2:1
2. 2:2
3. 1:2
4. 1:1

Q. The medians AL, BM and CN of a $\Delta ABC$ intersect at P. If AL = 5, then the length of AP is

1. $\frac{5}{13}$
2. $\frac{5}{4}$
3. $\frac{10}{3}$
4. $\frac{15}{2}$

Q. RC is the median and G is the centroid in the triangle, if RG is 2.5 cm what is the length of median RC.

1. 5
2. 7.5
3. 3.75
   
4. 4.5

Q. In an equilateral triangle of side 6 cm each median is drawn from a vertex of the triangle to its opposite side, find the length of the altitude.

Q. Centroid divides every median in ratio.

1. 2:1
2. 1:2
3. 1:3

Q. The centroid of a triangle is located 12 units from one of the vertices of a triangle. Find the length of the median of the triangle drawn from that same vertex.

1. 16 units
2. 24 units
3. 36 units
4. 18 units

Q. Construct the triangle with the following measurements and locate the centroid:
$△PQR$ with $\angle Q={90}^o$, $PQ=4.8cm$ and $QR=5.5cm$

Q. Construct the triangle with the following measurements and locate the centroid:
Isosceles $△$ with equal sides $5cm$ and base angles ${50}^o$.

Q. Draw a triangle ABC.
Draw its median CF

Q. Find centroid of a triangle $ABC$ with vertices $A(1,3),B(4,6)$ and $C(7,-3)$.

1. $(6,3)$
2. $(-5,6)$
3. $(-3,5)$
4. $(4,2)$

Q. Construct the triangle with the following measurements and locate the centroid:
$△KLM$ with $KL=6.1cm$, $LM=7.2cm$ and $\angle KLM={115}^o$

Q. In a triangle $ABC$, find the median where the line segment starts at $RC$.

1. $M_b$
2. $M_c$
3. $M_d$
4. $M_a$

Q.

The given triangle has Centroid at O.

If PC = 54 cm, Find the length of OC.

1. 18 cm

2. 42 cm

3. 24 cm

4. 36 cm

Q. In an equilateral triangle of side 6 cm each median is drawn from a vertex of the triangle to its opposite side, find the length of the altitude.

1. $\sqrt{4}5$
2. $\sqrt{2}7$
3. $\sqrt{3}0$
4. $\sqrt{2}5$