Question

Define the following terms: median and altitude.

Answer 1

Hint:
Here, we need to define the terms ‘median’ and ‘altitude’. We will define the terms and use an example to explain what is a median and altitude of a triangle respectively.

Complete step by step solution:
A median of a triangle ABC is the line segment drawn from a vertex to the opposite side, such that the side opposite to the vertex is bisected.
For example:
In the following triangle ABC, AD is the median drawn from vertex A, on the side opposite to A, that is BC. D lies on BC.

Here, AD bisects BC, that is BD \[ = \] CD.
A triangle can have at most three medians.

You can observe that in triangle ABC, AD is the median drawn from vertex A to side BC, such that BD \[ = \] CD.
BE is the median drawn from B to side AC, such that AE \[ = \] CE, and CF is the median drawn from vertex C to side AB, such that AF \[ = \] BF.
An altitude of a triangle ABC is the line segment drawn from a vertex to the opposite side, such that the side opposite to the vertex and altitude are perpendicular.
For example:
In the following triangle ABC, AD is the perpendicular drawn from vertex A, on the side opposite to A, that is BC. D lies on BC.

Here, AD is perpendicular to BC, that is \[\angle ADB = 90^\circ \].
A triangle can have at most three altitudes.

You can observe that in triangle ABC, AD is the altitude drawn from vertex A to side BC, such that \[\angle ADC = 90^\circ \].
BE is the altitude drawn from B to side AC, such that \[\angle BEC = 90^\circ \], and CF is the altitude drawn from vertex C to side AB, such that \[\angle CFA = 90^\circ \].

Note:
In the example provided for the median, we can see point G. The point G lies on the intersection of the three medians of the triangle. This point is the centroid of the triangle.
Similarly, in the example provided for altitude, you can see point G. The point G lies at the intersection of the three altitudes of the triangle. This point is known as the orthocentre of the triangle.