In what type of triangle is altitude and median the same?

equilateral triangle
However, in the case of an equilateral triangle, the median and altitude are always the same.

Is there a type of triangle that an angle bisector a median and an altitude are all on the same line?

No. Angle bisector which is also a median implies isosceles triangle which implies it is also the altitude.

In what type of triangle can a segment can be both an altitude and a median at the same time?

In fact, it only will in two types of triangles. In an equilateral triangle, all the angles are equal. Here, the altitude comes right down the middle and, in fact, is the same as the median. For an equilateral triangle, the median cuts the side in half and is the same as an altitude.

What kind of triangle has 3 angle bisectors that are also altitudes and medians?

In an equilateral triangle, the altitudes, the angle bisectors, the perpendicular bisectors, and the medians to each side coincide.

Where is the altitude of a 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).

Can the altitude and median be same for any triangle?

Yes, the altitude and median can be the same in a triangle. for example, consider an equilateral triangle, the median which divides the side in equal is also perpendicular to the side and hence the altitude and the median is the same.

What is median triangle?

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle’s centroid.

What is bisector in triangle?

An angle bisector of a triangle is a segment, ray or line which divides an angle of the triangle into two congruent (equal in measure) parts. Since all triangles have three angles, all triangles have three angle bisectors.

Are altitudes of a triangle equal?

According to the right triangle altitude theorem, the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse. For a right triangle, when a perpendicular is drawn from the vertex to the hypotenuse, two similar right triangles are formed.

Is bisector a midpoint?

Midpoints are points exactly in the middle of a segment: they’re equidistant to either end. Segment bisectors are lines that cut a segment right in half, which means they go through the midpoint of the segment.

What is altitude in triangle?

In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). The length of the altitude, often simply called “the altitude”, is the distance between the extended base and the vertex.

What are altitudes medians and angle bisectors of a triangle?

The altitudes, medians and angle bisectors of a Triangle are defined and problems along with their solutions are presented. The altitude of a triangle is a line through a given vertex of the triangle and perpendicular to the side opposite to the vertex.

Where do the three angle bisectors meet in a triangle?

The three angle bisectors meet in a single point inside the triangle. In general, altitudes, medians, and angle bisectors are different segments. In certain triangles, though, they can be the same segments. In Figure , the altitude drawn from the vertex angle of an isosceles triangle can be proven to be a median as well as an angle bisector.

When does the median and angle bisector interchange in an isosceles triangle?

The Median, angle bisector is the same in an isosceles triangle when the altitude is drawn from the vertex to the base. Altitude, median, angle bisector interchange in case of an isosceles triangle.

Where do the 3 medians of a triangle meet?

In every triangle, the three medians meet in one point inside the triangle (Figure 6). The three medians meet in a single point inside the triangle. Angle bisector. An angle bisector in a triangle is a segment drawn from a vertex that bisects (cuts in half) that vertex angle.