Where can the altitudes of a triangle intersect?

Where can the altitudes of a triangle intersect?

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

Where can the bisector of the angles of an obtuse triangle intersect?

The three angle bisectors of the angles of a triangle meet in a single point, called the incenter .

Can the altitude of an obtuse triangle be inside the triangle?

In a triangle, a line segment from a vertex and perpendicular to the opposite side is called an altitude. If the triangle is obtuse, then the altitude will be outside of the triangle. If the triangle is acute, then the altitude will be inside the triangle.

Where do the medians of an obtuse triangle intersect?

In an obtuse triangle, the altitudes intersect outside the triangle. 5. The medians of an obtuse triangle will always intersect inside the triangle.

Can altitudes intersect outside the 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. To make this happen the altitude lines have to be extended so they cross.

What is the location of the point of concurrence of altitudes in an obtuse angled triangle What is this point of concurrence called?

When the triangle is obtuse, the points of concurrency lie outside the triangle. The common intersection of the three lines containing the altitudes is called the orthocenter of a triangle.

Where can the perpendicular bisectors of an obtuse triangle intersect I Inside the triangle?

All three bisectors still meet at the same point, but in the acute triangle they meet at a point INSIDE the triangle; with the obtuse triangle they meet at a point OUTSIDE of it.

Where do altitudes meet for an obtuse triangle?

In an obtuse triangle, the altitudes meet outside of the triangle. The three altitude lines meet at a point called the Orthocenter.

How do you find the altitude of an obtuse triangle?

Method. The construction starts by extending the chosen side of the triangle in both directions. This is done because, this being an obtuse triangle, the altitude will be outside the triangle, where it intersects the extended side PQ. After that, we draw the perpendicular from the opposite vertex to the line.

Is an isosceles triangle the altitude and median are?

In an isosceles triangle, the altitude and median are the same line segment when drawn from the vertex opposite the base to the base.

Where is the median of a triangle?

A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex. The medians of a triangle are concurrent at a point. The point of concurrency is called the centroid.

Why do we draw the altitude of an obtuse triangle?

This is done because, this being an obtuse triangle, the altitude will be outside the triangle, where it intersects the extended side PQ. After that, we draw the perpendicular from the opposite vertex to the line. This is identical to the construction A perpendicular to a line through an external point.

Where do the altitudes of the different types of triangles meet?

Altitudes in right, acute, obtuse and equilateral triangles. An altitude of a triangle is a line segment through the vertex and perpendicular to the base. All three altitudes intersect at the same point called orthocenter. Right Triangle – has a 90 degree angle, altitudes meet at the vertex of the right angle

Which angle of the triangle is obtuse?

Angle C is obtuse The angle ACB is opposite the chosen vertex A, and is obtuse(greater than 90°). and is the reason the first step of the construction is to extend the base line, just in case this happens. The altitude meets the extendedbase BC of the triangle at right angles.

How do you construct an obtuse triangle from a graph?

The construction starts by extending the chosen side of the triangle in both directions. This is done because, this being an obtuse triangle, the altitude will be outside the triangle, where it intersects the extended side PQ. After that, we draw the perpendicular from the opposite vertex to the line.