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Basic Proportionality Theorem says: If a line is drawn parallel to one side of the triangle to intersect the other two sides at distinct points .Then the other two sides are divided in the same ratio.
PROOF ( to follow this proof, just draw the triangles and segments)
Draw triangle PQR and construct line L parallel to segment QR.
Line L intersects segment PQ and segment PR at S and T respectively.
We want to show that length of PS/ length of QS is equal to length PT/ length of PR since that is what the BPT says.
Construct segments SR and QT.
Look at triangles PTS and QTS and note they have the same height which implies that
the area of triangle PTS/ area of triangle QTS is equal to PS/ SQ.
By the same reasoning, the areas of triangle SPT/ triangle SRT is equal to PT/TR.
Triangles QTS and SRT both have the same height and both have ST as a base segment so they have the same area.
So the ratio of the area of triangle PTS to the area of triangle QTS is equal to the ratios of the area of triangles SPT/SRT.
So the ratio of PS/SQ is equal to PT/TR
Since line L which is parallel to segment QR divides segment PQ and segment PR in the same ratio we have proved the BPT.
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Why the Pythagorean Theory got his name?
the Pythagorean Theorem got its name from the man Pythagoras who came up with the theory.
Who developed the theory a plus b equals c?
A Mathematician named Pythagorean. That is why it is called Pythagorean's theorem. For every right triangle, this theorem will be true.
Why is Pythagoras theorem only a theory that can not be proven?
It can be proven to an extent but if the sides of a right angle triangle are equal in length then using Pythagoras' theorem is impossible to exactly find the length of its hypotenuse which will always be an irrational number that can't be determined.It is a theorem, not a theory. They are not the same. A theorem is shown to be true based on axioms, what is already known to be true. It does not need to be proven using a scientific method.
What is a famous math theory?
Do you mean THEOREM? In math a theorem is a statement which is proved true by applying a chain of logic. A famous one is the Pythagorean Theorem: The sum of squares of the legs of a right triangle equals the square of the hypotenuse. A^2 + B^2 = C^2
What is the theory of the sum of square of the two shorter sides is equal the square of the longest hypotenuse side?
This pertains to right angled triangles and is called the pythagoras theorem or theory
