Question

In the right triangle show below are any altitudes shown does lead to any generalizations about tight triangles explain your answer.

Answer 1

Yes altitudes are shown.

Two altitudes can be there depending upon the choice of base and altitude of triangle.

Explanation:

First of all, let us have a look at the definition of an altitude in a triangle.

Altitude of any triangle is the perpendicular dropped (making a right angle with the side) on any side opposite to a vertex of triangle.

Here, in the given
`\triangle ABC`, we can see that the
`\angle B` is right angle.

i.e. Altitudes are shown here.

Generalization about right triangles:

There can be two choices of altitudes in a right angled triangle depending upon the choice of base.

In the given triangle
`\angle B` is right angle.

If we choose AB as the base of triangle, the vertex opposite to AB is C.

The side BC is at right angle to AB i.e. perpendicular dropped from vertex C to side AB. Therefore BC is the altitude.

Now, If we choose BC as the base of triangle, the vertex opposite to BC is A.

The side AB is at right angle to CD i.e. perpendicular dropped from vertex A to side BC. Therefore AB is the altitude.