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

Construct two triangles in your notebook and find their centroid.

Accepted Answer

Steps of construction:

$1$ . Draw $△ P Q R$ .

$2$ . With $Q$ as centre and more than half of $Q R$ as radius, draw arcs above and below $Q R$ .

$3$ . Keeping same radius, with centre $R$ , draw arcs above and below $Q R$ such that both arcs intersect above and below respectively.

$4$ . Draw line between the intersection points such that it intersects $Q R$ at point $S$ . The line which intersects $Q R$ is the perpendicular bisector of $Q R$ . Join $P S$ . $P S$ is median of the triangle.

$5$ . Similarly, draw perpendicular bisector of side $P R$ . Join $Q V$ . $Q V$ is the median of the triangle.

$6$ . Similarly, draw perpendicular bisector of side $P Q$ . Join $R U$ . $R U$ is the median of the triangle.

Construction:

Clearly, the medians intersect at one point. Their point of concurrence is called centroid. It is denoted by $G$ .

Similarly, draw another triangle $X Y Z$ and draw the medians of the triangle $X P, Y Q$ and $Z R$ which meet at a common point called centroid represented by $G$ .

Construct two triangles in your notebook and find their centroid.

Important Questions on Properties of a Triangle

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