Question

Draw rough sketches for  $ \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  $ \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  $ \Delta XYZ $ as an obtuse angled triangle as shown in the figure.

Altitude (perpendicular line).

 $ YL =  $ exterior altitude of  $ \Delta XYZ $ .

Here,

In figure,  $ \Delta XYZ $ is obtuse angled triangle because we can only draw an exterior altitude from abuse angle it can observed that on  $ \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.