Question

Draw rough sketches for  $\mathrm{\Delta }XYZ$ such that YL is an altitude in the exterior of the triangle.

Answer 1

Hint: We can draw an altitude in the exterior of a triangle only if it is an obtuse angled triangle. By using this concept we draw the triangle first and then altitude to the exterior of a triangle.

Complete step by step solution:

We have to draw an altitude in the exterior of the  $\mathrm{\Delta }XYZ$ 

An altitude can be drawn in the exterior of a triangle only if it is an obtuse angled triangle.

So, we need to draw  $\mathrm{\Delta }XYZ$ as an obtuse angled triangle as shown in the figure.

Altitude (perpendicular line).

 $YL=$ exterior altitude of  $\mathrm{\Delta }XYZ$ .

Here,

In figure,  $\mathrm{\Delta }XYZ$ is obtuse angled triangle because we can only draw an exterior altitude from abuse angle it can observed that on  $\mathrm{\Delta }XYZ,YZ$ is an altitude drawn interior to side  $XZ$ which is extends up to point  $L.$ 

Note: To know whether the altitude will be on the exterior of a triangle or in the interior of a triangle, we need to know the properties of the triangle.

For an acute angled triangle, the altitude will be in the interior of a triangle.

For a right angled triangle, the altitude will be at the angle which is right angled.