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Prove that the three times the sum of squares of sides of triangle is equal to four times of its median?
Let the triangle be ABC and its medians by AX and BY and CZ.
Therefore, since AC=AB, and OP=BD.
Therefore,
By Triangle Equiangular Property,
Triangle ABC simliar to Triangle XYZ
Therefore,
Three times the sum of the squares of sides of triangle equal to 4 times of its median.:)
Hope it helped.
What else can I help you with?
What is equal to the hypotenuse of a right triangle?
sum of squares of opposite sides
Pythagorean theorem says that the triangle is a?
A triangle is a right triangle if the sum of the squares of the two legs is equal to the square of the hypotenuse.
How is the altitude and a median of a triangle the same?
they are the same because the triangles side is equal
Which segment always divides a triangle into two triangles of equal areas?
median
Can a median divide a triangle in equal area?
Sure. That's true of a median in every isosceles triangle, and every median in an equilateral triangle. In fact it is true for any median of any triangle. The two parts may not be the same shapes but they will have the same area. That is why the point where the three medians meet (centroid) is the centre of mass of a triangular lamina of uniform thickness.
What median of an isosceles triangle is the same segment in the triangle as the leg bisector hypotenuse altitude?
It is the median which divides the side which is not one of the equal sides.
Can the altitude from the vertex angle of an isosceles triangle be the median?
If the triangle is really isosceles, and it's not lying on one of the equal sides, then the altitude is always a median.
What is equal to the hypotenuse of a right triangle?
sum of squares of opposite sides
Pythagorean theorem says that the triangle is a?
A triangle is a right triangle if the sum of the squares of the two legs is equal to the square of the hypotenuse.
Definition of converse for pythagorean theroem?
Pythagorean Theorem: In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.Converse: If the square on the hypotenuse is equal to the sum of the squares on the other two sides of a triangle, then it is a right triangle.
Which segment always divides a triangle into two triangles of equal areas?
median
How is the altitude and a median of a triangle the same?
they are the same because the triangles side is equal
Can the median of an equilateral triangle be longer than its altitude?
For the equilateral triangle in Euclidean space(i.e, the triangles you see in general) median is the same as its altitude. So, both are of equal length.
In a right triangle the sum of the squares of the leg lengths is equal of the lengths is equal to the square of the hypotenuse?
Yes
Can a median divide a triangle in equal area?
Sure. That's true of a median in every isosceles triangle, and every median in an equilateral triangle. In fact it is true for any median of any triangle. The two parts may not be the same shapes but they will have the same area. That is why the point where the three medians meet (centroid) is the centre of mass of a triangular lamina of uniform thickness.
How do you prove that a triangle is a right triangle?
all the angles add up to 180 degreespythagorean theorem. if it works, you have a right angle triangle. a^2 + b^2 = c^2. the sum of the squares of the two shorter sides is equal to the square of the longest side, also known as the hypotenuse.
The square of the hypotenuse is equal to the sum of the squares of the other two sides of what kind of triangle?
right angle triangle
