Altitude of a triangle definition

The altitude of a triangle is the perpendicular line segment drawn from the vertex to the opposite side of the triangle. It may lie inside or outside the triangle, based on the types of triangles.

Triangles contain special segments like perpendicular bisector, median, and altitude. When you think of altitude, you may think of the increasing elevations of mountain ranges; the term altitude also has its place in Geometry, however, and it refers to the height of a triangle. Explore our app and discover over 50 million learning materials for free. In this article, we will understand the concept of altitudes in triangles and their related terms in detail. We will learn how to calculate the altitude with respect to different types of triangles.

Altitude of a triangle definition

The altitude of a triangle is a line from a vertex to the opposite side, that is perpendicular to that side, as shown in the animation above. A triangle therefore has three possible altitudes. The altitude is the shortest distance from a vertex to its opposite side. The word 'altitude' is used in two subtly different ways: It can refer to the line itself. For example, you may see "draw an altitude of the triangle ABC". As a measurement. You may see "the altitude of the triangle is 3 centimeters". In this sense it is used in way similar to the "height" of the triangle. In most cases the altitude of the triangle is inside the triangle, like this: Angles B, C are both acute However, if one of the angles opposite the chosen vertex is obtuse , then it will lie outside the triangle, as below. Angle C is obtuse The altitude meets the extended base BC of the triangle at right angles. In the animation at the top of the page, drag the point A to the extreme left or right to see this. It turns out that in any triangle, the three altitudes always intersect at a single point, which is called the orthocenter of the triangle. For more on this, see Orthocenter of a triangle. The following two pages demonstrate how to construct the altitude of a triangle with compass and straightedge. Constructing the altitude of a triangle altitude inside.

If one angle is a right angle, the orthocenter coincides with the vertex at the right angle. Start learning with StudySmarter, the only learning app you need. The altitudes of various types of triangles have some properties that are specific to certain triangles.

In geometry , an altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the side opposite the vertex. This line containing the opposite side is called the extended base of the altitude. The intersection of the extended base and the altitude is called the foot of the altitude. The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as dropping the altitude at that vertex.

Height of a triangle or the line segment from a vertex and perpendicular to the opposite side. In a triangle, a line segment from a vertex and perpendicular to the opposite side is called an altitude. It is also called the height of a triangle. The red lines below are all altitudes. When a triangle is a right triangle, the altitude, or height, is the leg. 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. What if you were given one or more of a triangle's angle measures? How would you determine where the triangle's altitude would be found?

Altitude of a triangle definition

In geometry, the altitude of a geometric figure generally refers to a perpendicular distance measured from the base of the figure to its opposite side. The term altitude is often used interchangeably with "height. The dotted red lines in the figures above represent their altitudes. Note that the altitude can be depicted at multiple points within the figures, not just the ones specifically shown. Altitude in triangles is defined slightly differently than altitude in other geometric figures. In other geometric figures, such as those shown above except for the cone , the altitude can be formed at multiple points in the figure. In a triangle however, the altitude must pass through one of its vertices , and the line segment connecting the vertex and the base must be perpendicular to the base. In other words, an altitude in a triangle is defined as the perpendicular distance from a base of a triangle to the vertex opposite the base. An altitude of the isosceles triangle is shown in the figure below:. Since all triangles have 3 vertices, every triangle has 3 altitudes, as shown in the figure below:.

Coba sushi restaurant

Nie wieder prokastinieren mit unseren Lernerinnerungen. The formula for an altitude of a triangle varies for different triangles. Save explanations to your personalised space and access them anytime, anywhere! By registering you get free access to our website and app available on desktop AND mobile which will help you to super-charge your learning process. Explore our app and discover over 50 million learning materials for free. Math Geometry Altitude Altitude. What is the rules in finding the altitude of a triangle? What is the property of the altitude of a triangle? Their History and Solution". Now the perimeter of an equilateral triangle is 3x. Flashcards in Altitude 7 Start learning. Post My Comment. Consider an arbitrary triangle with sides a, b, c and with corresponding altitudes h a , h b , h c. We can calculate the coordinates of the orthocenter using the vertex coordinates of the triangle.

The altitude of a triangle , or height , is a line from a vertex to the opposite side, that is perpendicular to that side.

Everything you need to know on. Toggle limited content width. Download as PDF Printable version. Altitude of Triangle Formula 4. Since there are three sides in a triangle, three altitudes can be drawn in it. Let's take a look at how it may look. A triangle in which all three sides are equal is called an equilateral triangle. Altitude of a Triangle Examples Example 1: The area of a triangle is 72 square units. Q4 What is the property of the altitude of a triangle? In a right triangle the three altitudes h a , h b , h c the first two of which equal the leg lengths b and a respectively are related according to [34] [35]. Create your free account now. Geometrie der Stellung. However, they are different from each other in many ways. Start Quiz. Will you pass the quiz?