Name: Special Points of Concurrency
Uploaded: 2019-07-19
Duration: 8 min 2 s
Description: You may have heard about the special points of concurrency such as incentre, circumcentre, centroid, and orthocentre. Watch this video to learn about them in...

Question

Identify the median and altitude in the following triangle.

Accepted Answer

We know that the altitude of a triangle is the perpendicular that is drawn from the vertex of a triangle to the opposite side.

Here, we observe that $A D$ is perpendicular from the vertex $A$ on the opposite side $B C$ . Hence, $A D$ is the altitude of the triangle.

Also, we know that the median of a triangle is the line segment from a vertex to the midpoint of the opposite side of the triangle.

We observe that in the given triangle, $Q S = S R$ . This means $S$ is the mid-point of $Q R$ . So, the line joining the vertex $P$ and the mid-point $S$ is the median of the triangle. Hence, $P S$ is the median of the triangle.

In $△ A B D$ and $△ A C D$ , we have,

$A B = A C = 4 cm$ [Given]

$A D = A D$ [Common side]

And, $∠ A D B = ∠ A D C$ [Both are $90 °$ ]

Hence, $△ A B D ≅ △ A C D$ [By SSA criterion of congruency of triangles]

So, we have, $B D = C D$ [CPCT]

This means the point $D$ is also the mid-point of the side $B C$ .

Hence, $A D$ is also the median of the triangle.

Therefore, $A D$ is both the median and the altitude of the triangle.

Identify the median and altitude in the following triangle.

Important Questions on Triangle and Its Properties

Learn and Prepare for any exam you want !