Straight lines defined for 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. 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. It is a special case of orthogonal projection. Altitudes can be used in the computation of the area of a triangle: one half of the product of an altitude's length and its base's length equals the triangle's area. Thus, the longest altitude is perpendicular to the shortest side of the triangle. The altitudes are also related to the sides of the triangle through the trigonometric functions. In an isosceles triangle (a triangle with two congruent sides), the altitude having the incongruent side as its base will have the midpoint of that side as its foot. Also the altitude having the incongruent side as its base will be the angle bisector of the vertex angle. It is common to mark the altitude with the letter h (as in height), often subscripted with the name of the side the altitude is drawn to. In a right triangle, the altitude drawn to the hypotenuse c divides the hypotenuse into two segments of lengths p and q. If we denote the length of the altitude by hc, we then have the relation (Geometric mean theorem) For acute triangles the feet of the altitudes all fall on the triangle's sides (not extended). In an obtuse triangle (one with an obtuse angle), the foot of the altitude to the obtuse-angled vertex falls in the interior of the opposite side, but the feet of the altitudes to the acute-angled vertices fall on the opposite extended side, exterior to the triangle. This is illustrated in the adjacent diagram: in this obtuse triangle, an altitude dropped perpendicularly from the top vertex, which has an acute angle, intersects the extended horizontal side outside the triangle. (Wikipedia).
This video defines an altitude and orthocenter of a triangle. Complete Video List: http://mathispower4u.yolasite.com/
From playlist Relationships with Triangles
Altitude of a Triangle - Finding The Orthocenter
This geometry video tutorial provides a basic introduction into the altitude of a triangle. It provides the definition of an altitude and it includes plenty of examples of finding the orthocenter of an acute triangle, right triangle, and an obtuse triangle. Geometry Playlist: https://w
From playlist Geometry Video Playlist
Constructing an Altitude of a Triangle
This video shows how to construct the altitude of a triangle using a compass and straightedge. Complete Video List: http://mathispower4u.yolasite.com/
From playlist Relationships with Triangles
What are Altitudes in a Triangle? (In depth explanation) | Don't Memorise
To learn more about Triangles enroll in our full course now: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&utm_campaign=DM&utm_content=p_63OpLr23Y&utm_term=%7Bkeyword%7D In this video, we will learn: 0:00 what are altitudes? 0:57 orthocenter of a triangle 1:
From playlist Middle School Math - Triangles
Geometry - Basic Terminology (21 of 34) The Altitude (Height) of a Right Triangle
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain how every right triangle has 3 altitudes (or heights). Next video in the Basic Terminology series can be seen at: http://youtu.be/ySUriT4LxPc
From playlist GEOMETRY 1 - BASIC TERMINOLOGY
Altitudes of Triangles and Orthocenter
I introduce altitudes in triangles and point of concurrency, the orthocenter. I finish by working through two examples, the last of which finding the orthocenter given the three vertices of a triangle. EXAMPLES AT 7:10 10:31 Find free review test, useful notes and more at http://www.math
From playlist Geometry
Constructing the Altitude of a Triangle Using Geometer's Sketchpad
This video shows how to construct the altitude of a triangle using geometer's sketchpad. Complete Video List: http://mathispower4u.yolasite.com/
From playlist Relationships with Triangles
How to determine the height of a triangle when given the area
👉 Learn how to find the area and perimeter of triangles. A triangle is a shape of three sides. The area of a shape is the measure of the portion enclosed by the shape while the perimeter of a shape is the measure of the outline enclosing the shape. The area of a triangle is given by half
From playlist Area and Perimeter
Ex: Related Rates - Area of Triangle
This video provides an example of how to solve a related rates problem involving the area of a triangle and rate of change of the base. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Related Rates
Geometric Properties of an Equilateral Triangle
This lecture explores a few geometric properties of equilateral triangles, such as proving that the altitude splits an equilateral triangle into two congruent triangles. Further, the altitude, median, and angle bisector are shown to be the same. Finally, the altitude is used to derive a 30
From playlist Geometry
The Three / Four bridge in Triangle Geometry: Incentres and Orthocentres | Six 6 | Wild Egg
We look at how to cross the Three / Four bridge geometrically: in both directions. This connects with some classical triangle geometry, involving triangle centres going back to ancient Greek geometry. We will touch base with the algebraic orientation to angle bisection, modifying a little
From playlist Six: An elementary course in Pure Mathematics
What are the special segments of similar triangles
👉 Learn how to solve with similar triangles. Two triangles are said to be similar if the corresponding angles are congruent (equal). Note that two triangles are similar does not imply that the length of the sides are equal but the sides are proportional. Knowledge of the length of the side
From playlist Similar Triangles
https://sites.google.com/site/praxishelp/ geometry help
From playlist Praxis Test Help
Altitude Rule for Right Triangles - Geometry
This video teaches students how to use the altitude rule to find the missing side of a right triangle. In particular, I explore the 3 similar triangles that are created when we construct an altitude from a right angle. The problem covered in this video utilizes the altitude of the origina
From playlist Geometry
Altitude Geometric Mean Theorem
Learn how to use the Altitude Geometric Mean Theorem in this free math video tutorial by Mario's Math Tutoring. 0:09 What is the Geometric Mean 1:08 Using Similar Triangles to Show Why the Altitude Geometric Mean Theorem Works 1:49 Example 1 Solving for the Altitude 2:17 Example 2 Solving
From playlist Geometry
Classifying triangles by the measure of their sides
👉 Learn all about classifying triangles. A triangle is a closed figure with three sides. A triangle can be classified based on the length of the sides or based on the measure of the angles. To classify a triangle based on the length of the sides, we have: equilateral (3 sides are equal), i
From playlist Triangles
Incenter, Circumcenter, Orthocenter & Centroid of a Triangle - Geometry
This geometry video tutorial explains how to identify the location of the incenter, circumcenter, orthocenter and centroid of a triangle. The incenter can be found be drawing the 3 angle bisectors of a triangle and identifying the point of intersection. The incenter always lie inside of
From playlist Geometry Video Playlist