Sage-Tips

Does the altitude always pass through the vertex?

No matter where we move the points of the triangle, the altitude is always a segment that is perpendicular to the base and passes through the vertex. It might even coincide with one of the sides of the triangle. An altitude may be inside, outside, or one of the sides of a triangle.

Does the altitude have to be inside the triangle?

The altitude of a triangle is the perpendicular distance from the base to the opposite vertex. It always lies inside the triangle.

Can altitude go outside the triangle?

An altitude of a triangle is the perpendicular segment from a vertex of a triangle to the opposite side (or the line containing the opposite side). An altitude of a triangle can be a side or may lie outside the triangle.

Can all three altitudes fall outside of a triangle?

It turns out that all three altitudes always intersect at the same point – the so-called orthocenter of the triangle. The orthocenter is not always inside the triangle. If the triangle is obtuse, it will be outside.

What will always pass through the vertex of a triangle?

The centroid is always in the interior of the triangle. The altitude of a triangle is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. There are therefore three altitudes possible, one from each vertex.

Can the altitude and median be same for a triangle?

The answer is No. The altitude and median is not the same thing in a triangle. However, in the case of an equilateral triangle, the median and altitude are always the same.

Are altitude of a triangle congruent?

A Proof that lines of the three altitudes of a triangle are concurrent. Given triangle ABC, E is constructed to be the midpoint of AB and line EF is constructed be perpendicular to AB. Thus any point F is equidistant from A and B. Thus, triangles AEF and BEF are congruent by SAS.

How many altitude Can a triangle have?

three altitudes
The three altitudes of a triangle intersect at the orthocenter, which for an acute triangle is inside the triangle.