Name: The Altitude of a Triangle
Uploaded: 2019-07-19
Duration: 2 min 45 s
Description: The orthocentre is made by intersecting the altitudes drawn from all the vertices to the triangle's opposite sides. But what is altitude? Watch this video to...

Question

Some triangles are given below and their medians are drawn. Fill up the blanks in the table accordingly.

Figure	Name	Distance of centroid $G$ from the vertex	Distance of midpoint of opposite side	Ratio
$1$	$△ A B C$	$A G = 2.2 cm$ $B G = 3 cm$ $C G = 3.4 cm$	$G D = 1.1 cm$ $G E = 1.5 cm$ $G F = 1.7 cm$	$A G : G D = 2 : 1$ $B G : G E = 2 : 1$ $C G : G F = 2 : 1$
$2$	$△ P Q R$	$P G =$ _____ $Q G =$ _____ $R G =$ _____	$G S =$ _____ $G T =$ _____ $G U =$ _____	$P G : G S =$ _____ $Q G : G T =$ _____ $R G : G U =$ _____
$3$	$△ D E F$	$D G =$ _____ $E G =$ _____ $F G =$ _____	$G L =$ _____ $G M =$ _____ $G N =$ _____	$D G : G L =$ _____ $E G : G M =$ _____ $F G : G N =$ _____
$4$	$△ X Y Z$	$X G =$ _____ $Y G =$ _____ $Z G =$ _____	$G F =$ _____ $G E =$ _____ $G D =$ _____	$X G : G F =$ _____ $Y G : G E =$ _____ $Z G : G D =$ _____

Accepted Answer

Here the point $G$ in all above triangles is centroid of the triangle.

On measuring the dimensions of the above triangles, the table is updated as below:

Figure

Name

Distance of centroid $G$ from the vertex

Distance of mid-point of opposite side

Ratio

$1$

$△ A B C$

$A G = 2.2 cm$

$B G = 3 cm$

$C G = 3.4 cm$

$G D = 1.1 cm$

$G E = 1.5 cm$

$G F = 1.7 cm$

$A G : G D = 2 : 1$

$B G : G E = 2 : 1$

$C G : G F = 2 : 1$

$2$

$△ P Q R$

$P G = 2.2 cm$

$Q G = 3 cm$

$R G = 3.4 cm$

$G S = 1.1 cm$

$G T = 1.5 cm$

$G U = 1.7 cm$

$P G : G S = 2 : 1$

$Q G : G T = 2 : 1$

$R G : G U = 2 : 1$

$3$

$△ D E F$

$D G = 4 cm$

$E G = 4 cm$

$F G = 4.4 cm$

$△ X Y Z$

$G M = 2 cm$

$G N = 2.2 cm$

$D G : G L = 2 : 1$

$E G : G M = 2 : 1$

$F G : G N = 2 : 1$

$4$

$△ X Y Z$

$X G = 2.4 cm$

$Y G = 3.6 cm$

$Z G = 4.4 cm$

$G F = 1.2 cm$

$G E = 1.8 cm$

$G D = 2.2 cm$

$X G : G F = 2 : 1$

$Y G : G E = 2 : 1$

$Z G : G D = 2 : 1$

Chhattisgarh Board Solutions for Chapter: Properties of a Triangle, Exercise 2: Activity

Chhattisgarh Board Mathematics Solutions for Exercise - Chhattisgarh Board Solutions for Chapter: Properties of a Triangle, Exercise 2: Activity

Questions from Chhattisgarh Board Solutions for Chapter: Properties of a Triangle, Exercise 2: Activity with Hints & Solutions

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