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May 30, 2018 · Aprendește teorema medianei și reciproca teorema medianei pentru triunghi dreptunghic. Vezi formule, exemple și comentarii pe blogul profesorului Jitaru Ionel.
În geometria plană, teorema medianei stabilește o relație între lungimea unei mediane dintr-un triunghi și lungimile laturilor triunghiului. Teorema medianei este un caz particular al teoremei lui Stewart. Mai este numită teorema lui Apoloniu după Apoloniu din Perga.
- Definition
- Properties
- Formulas
The median of a triangle is a line segment that joins a vertex to the midpoint of the side that is opposite to that vertex.
Each triangle has 3 medians, one coming from each vertex; in △ABC, AD, BF, and CE are the 3 mediansThe 3 medians meet at a common point, called the centroid of the triangle. The centroid is the center of gravity or center of mass of the triangle; the three medians, ma, mb, & mcmeet at point O, w...Each median divides the main triangle into 2 smaller triangles having equal area. Thus, the 3 medians divide the main triangle into 6 smaller triangles having equal area; median AD forms triangles...How to Find the Median of a Triangle
A theorem called Apollonius’s Theorem gives the length of the median of a triangle. According to the theorem: ‘the sum of the squares of any two sides of a triangle equals twice the square on half the third side and twice the square on the median bisecting the third side’. Accordingly, the standard formulas for finding the medians of a triangle are given below: Let us solve some examples involving different types of triangles.
Fie ABC un triunghi dreptunghic în A și M mijlocul ipotenuzei (BC). Vom numi AM mediana corespunzătoare ipotenuzei sau mediana relativă la ipotenuză. Teo...
May 8, 2024 · A median A_1M_1 of a triangle DeltaA_1A_2A_3 is the Cevian from one of its vertices A_1 to the midpoint M_1 of the opposite side. The three medians of any triangle are concurrent (Casey 1888, p. 3), meeting in the triangle centroid (Durell 1928) G, which has trilinear coordinates 1/a:1/b:1/c. In addition, the medians of a triangle divide one another in the ratio 2:1 (Casey 1888, p. 3). A ...
Nov 21, 2023 · The median divides the opposite side into two segments of equal length. Furthermore, it divides the triangle into two triangles of equal size. The three medians of a triangle always meet at a ...
