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Proof Converse of Pythagoras Theorem Video Lecture | Crash Course for UAE Grade 10
FAQs on Proof Converse of Pythagoras Theorem Video Lecture - Crash Course for UAE Grade 10
| 1. What is the converse of the Pythagoras Theorem? |  |
Ans. The converse of the Pythagoras Theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
| 2. How can the converse of the Pythagoras Theorem be proved? | |
Ans. The converse of the Pythagoras Theorem can be proved by assuming that the given triangle is not a right triangle and then showing that the sum of the squares of the two shorter sides is not equal to the square of the longest side. If the assumption leads to a contradiction, then the original assumption that the triangle is not a right triangle is false, and hence the triangle must be a right triangle.
| 3. Can the converse of the Pythagoras Theorem be used to prove the original theorem? | |
Ans. No, the converse of the Pythagoras Theorem cannot be used to prove the original theorem. While the converse states that if the condition holds, then the triangle is a right triangle, it does not provide a way to prove that the condition will always hold. The original theorem, on the other hand, provides a direct relationship between the sides of a right triangle and can be proven using various geometric methods.
| 4. What is the importance of the converse of the Pythagoras Theorem? | |
Ans. The converse of the Pythagoras Theorem is important because it allows us to determine if a triangle is a right triangle or not. This can be useful in various applications, such as construction, engineering, and navigation, where right triangles play a significant role. By applying the converse, we can quickly identify right triangles and utilize their properties in solving problems or making accurate measurements.
| 5. Are there any other theorems related to the Pythagoras Theorem? | |
Ans. Yes, there are several other theorems related to the Pythagoras Theorem. Some of the notable ones include the Pythagorean triplets theorem, which states that if (a, b, c) is a set of positive integers satisfying a^2 + b^2 = c^2, then (ka, kb, kc) is also a set of positive integers satisfying the same equation, where k is any positive integer. Another theorem is the Converse of the Pythagorean Theorem, which states that if (a, b, c) is a set of positive integers satisfying a^2 + b^2 = c^2, then the triangle with sides a, b, and c is a right triangle.
Text Transcript from Video
hello friends this video on triangles
part 39 is brought you by exam fear calm
no more fear from exam before watching
this video please make sure that you
have watched part 1 - part 38 can we go
- let's try to converse of my choice
so in a triangle if square on one side
is equal to sum of the squares other two
sides then it is a very trying that
ocean sea is a given E Plus V Z square
DZ that is what this is called converged
of Pythagoras to do this let's draw one
triangle ABC was given where VC is equal
to RQ and AV is equal to EC innocent -
this length is equal to this then this
mind if you can prove that ABC is
congruent to PQ R that means this is
offering you all right
so the our goal here is to prove that
person right construction construction
what we have done so that B's benignly
be able to do that or similar does much
anything think you should stick in this
time maybe no that's 90 degree we know
this so we can apply whatever us so we
get plus R is equal to VM square da
about this right now T Q is equal to AV
so very AV square
RQ is nothing but easy so Alec use
nothing but VC VC square we can write
this a t-square BC square is already
given so right here these clans Gordie
Pierce per correct if he/she scramble to
pierce whereas their side sides are just
positive therefore EC is equal to P R
now you see this triangle this sides may
already well and I'm saying AC those are
equal to here correct
so in triangle ABC and our AV is equal
to VC is equal to R given AC is equal to
V our room right from equation x equals
1 so from there for triangle ABC is
congruent to triangle PQR if they're
complement this is Q is 90 be lots of it
therefore he is and that is what we
supposed rule and hence we have a very
simple English cost of 1000 triangle
where VC is equal to Q R and M is equal
to PB this is my D and then we prove
that both the angles thank you
visit exam viacom to watch free
education videos try free online tests
get the best quality study materials
study from the best tutors and mentors
and much more thanks annsofi
part 39 is brought you by exam fear calm
no more fear from exam before watching
this video please make sure that you
have watched part 1 - part 38 can we go
- let's try to converse of my choice
so in a triangle if square on one side
is equal to sum of the squares other two
sides then it is a very trying that
ocean sea is a given E Plus V Z square
DZ that is what this is called converged
of Pythagoras to do this let's draw one
triangle ABC was given where VC is equal
to RQ and AV is equal to EC innocent -
this length is equal to this then this
mind if you can prove that ABC is
congruent to PQ R that means this is
offering you all right
so the our goal here is to prove that
person right construction construction
what we have done so that B's benignly
be able to do that or similar does much
anything think you should stick in this
time maybe no that's 90 degree we know
this so we can apply whatever us so we
get plus R is equal to VM square da
about this right now T Q is equal to AV
so very AV square
RQ is nothing but easy so Alec use
nothing but VC VC square we can write
this a t-square BC square is already
given so right here these clans Gordie
Pierce per correct if he/she scramble to
pierce whereas their side sides are just
positive therefore EC is equal to P R
now you see this triangle this sides may
already well and I'm saying AC those are
equal to here correct
so in triangle ABC and our AV is equal
to VC is equal to R given AC is equal to
V our room right from equation x equals
1 so from there for triangle ABC is
congruent to triangle PQR if they're
complement this is Q is 90 be lots of it
therefore he is and that is what we
supposed rule and hence we have a very
simple English cost of 1000 triangle
where VC is equal to Q R and M is equal
to PB this is my D and then we prove
that both the angles thank you
visit exam viacom to watch free
education videos try free online tests
get the best quality study materials
study from the best tutors and mentors
and much more thanks annsofi
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