 science space and astronomy

# Can an altitude be a median?

Last Updated: 25th January, 2020

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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.

Hereof, can a median also be an altitude?

Yes. A median connects the midpoint of a triangle with the opposite vertex. An altitude connects a vertex of a triangle to the side opposite of the vertex so the angle formed between the two segments is a right angle.

Also, is the altitude of an equilateral triangle also the median? – If median drawn from vertex A is also the angle bisector, the triangle is isosceles such that AB = AC and BC is the base. Hence this median is also the altitude. In an equilateral triangle, each altitude, median and angle bisector drawn from the same vertex, overlap.

Additionally, what is the difference between an altitude and a median?

An altitude of a triangle is the perpendicular drawn from any vertex to it's opposite side whereas a median of a triangle is the line joining any vertex and the mid point of it's opposite side. In the case of an equilateral triangle median and altitude coincide with each other.

Is median perpendicular?

1 Answer. Segment joining a vertex to the mid-point of opposite side is called a median. Perpendicular from a vertex to opposite side is called altitude. A Line which passes through the mid-point of a segment and is perpendicular on the segment is called the perpendicular bisector of the segment. Professional

## Are altitudes perpendicular?

Altitudes are always perpendicular to their base. If the opposite corner isn't "above" the base, the altitude goes from the vertex to an imaginary line extended from the segment that forms the triangle's base. Professional

## Is a bisector always perpendicular?

When it is exactly at right angles to PQ it is called the perpendicular bisector. In general, 'to bisect' something means to cut it into two equal parts. The 'bisector' is the thing doing the cutting. With a perpendicular bisector, the bisector always crosses the line segment at right angles (90°). Explainer

## Is altitude always 90 degree?

In geometry, the altitude is a line that passes through two very specific points on a triangle: a vertex, or corner of a triangle, and its opposite side at a right, or 90-degree, angle. This is because it touches a vertex of the triangle. Explainer

## Is the altitude of an isosceles triangle also the median?

Because of this, the altitude that runs from A to the base intersects the base at its midpoint, making it the median from A to the base as well. Therefore, in an isosceles triangle, the altitude and median are the same line segment when drawn from the vertex opposite the base to the base. Pundit

## Is the median 90 degrees?

Median - A line segment that joins the vertice of a triangle to the midpoint of opposite side. Perpendicular bisector - A line segment that makes an angle of 90 deg (right angle) with the side of a triangle. The common point where the medians intersect is the centroid. Pundit

## Do altitudes bisect sides?

An altitude from a vertex bisects the opposite base if and only if the two sides emerging from that particular vertex are equal(not necessary in a right angle triangle). Therefore, you need to specify this condition before assuming that the altitude cuts the opposite base in half. Pundit

## What do you mean by altitude?

As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context. Pundit

## What is the median and altitude of a triangle?

key idea. A median of a triangle is a segment connecting a vertex to the midpoint of its opposite side. An altitude of a triangle is a segment from a vertex to the line containing its opposite side, and is perpendicular to that line. Pundit

## Does median bisect the base?

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. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length. The concept of a median extends to tetrahedra. Teacher

## What are the properties of altitude?

Properties of Altitudes of a Triangle
The altitude is the shortest distance from the vertex to its opposite side. The 3 altitudes always meet at a single point, no matter what the shape of the triangle is. The point where the 3 altitudes meet is called the ortho-centre of the triangle. Teacher

## What is a perpendicular bisector of a triangle?

The perpendicular bisector of a side of a triangle is a line perpendicular to the side and passing through its midpoint. The three perpendicular bisectors of the sides of a triangle meet in a single point, called the circumcenter . Teacher

## How do you find the Orthocenter?

Orthocenter of a Triangle
1. Find the equations of two line segments forming sides of the triangle.
2. Find the slopes of the altitudes for those two sides.
3. Use the slopes and the opposite vertices to find the equations of the two altitudes.
4. Solve the corresponding x and y values, giving you the coordinates of the orthocenter. Teacher

## What is the altitude of a 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). This line containing the opposite side is called the extended base of the altitude. Reviewer

## What is the altitude of isosceles triangle?

The altitude to the base of an isosceles triangle bisects the vertex angle. The altitude to the base of an isosceles triangle bisects the base. When the altitude to the base of an isosceles triangle is drawn, two congruent triangles are formed, proven by Hypotenuse - Leg. Reviewer

## How many exterior angles does a triangle have?

6 exterior angles Reviewer

## What is a scalene triangle?

Scalene Triangle. A scalene triangle is a triangle that has three unequal sides, such as those illustrated above. SEE ALSO: Acute Triangle, Equilateral Triangle, Isosceles Triangle, Obtuse Triangle, Triangle. CITE THIS AS: Weisstein, Eric W. " Reviewer

## What is the median in math?

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. If no number in the list is repeated, then there is no mode for the list. Supporter

## Is an altitude always an angle bisector?

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. Supporter

## How do you find the median of an equilateral triangle?

so in figure angle OCB is 30 degree as angle ACB is 60 degree( equilateral triangle). so basically to find length of median you need to find the length of line segment AB , and AB=AO+OB , and AO= 32 cm (given) , so you just need to find length of OB. OB= 32*(1/2)= 16 cm . so length of median AB is 16 +32 =48 cm. Co-Authored By:

#### EveryThingWhat Staff Editor

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25th January, 2020

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