PDF chapter test

Altitude position differs for various types of triangle.  Let us discuss its types:
• Acute angled triangle
• Right angled triangle
• Obtuse angled triangle
• Equilateral triangle and
• Isosceles triangle

Altitude in acute angled triangle:
All three altitude lies inside the triangle. Here $$ABC$$ is an acute-angled triangle and $$AF, BD$$ and $$CE$$ are the altitudes of the triangle $$ABC$$ and all three altitudes lies inside the triangle.

Altitude in right angled triangle:
The altitude perpendicular to the hypotenuse lies inside the triangle, but the other two altitudes are the legs of the triangle. Here $$ABC$$ is a right-angled triangle, and $$BD$$ is the altitude perpendicular to the hypotenuse lies inside the triangle, but the other two altitudes $$AB$$ and $$BC$$ are the legs of the triangle.

Altitude in obtuse angled triangle:
The altitude connected to the obtuse vertex lies inside the triangle, but the two altitudes connected to the acute vertices are outside the triangle. Here $$ABC$$ is an obtuse-angled triangle, and $$AF$$ is the altitude connected to the obtuse vertex lies inside the triangle, but the other two altitudes $$BD$$ and $$CE$$ connected to the acute vertices are outside the triangle.

Altitude in equilateral triangle:
The altitudes of an equilateral triangle bisect its base and the opposite angle. Here $$ABC$$ is an equilateral triangle and $$AF, BD$$ and $$CE$$ are the altitudes lie inside the triangle as it an acute-angled triangle. Also, altitudes of an equilateral triangle bisect its base and the opposite angle. For an equilateral triangle, the all three lines $$AF, BD$$ and $$CE$$ are altitudes, medians as well as angle bisector of the triangle $$ABC$$.

Altitude in isosceles angled triangle:
The altitudes of an isosceles triangle bisect its unequal base and the opposite angle. But this will not suit for other $$2$$ altitudes. Here $$ABC$$ is an isosceles triangle and $$AF, BD$$ and $$CE$$ are the altitudes of the triangle.  Also, altitudes of an isosceles triangle bisect its unequal base $$BC$$ and the opposite angle $$A$$, but this will not be true for the equal bases $$AC$$ and $$AB$$ and the opposite angles $$B$$ and $$C$$.