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Albert1
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A trapezoid ABCD ,AB//CD ,AD=BC
Prove :
$AC^2=AD^2+(AB).(CD)$
Prove :
$AC^2=AD^2+(AB).(CD)$
Prove: (AC)² = (AD)² + (AB)·(CD)
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In summary, the equation (AC)² = (AD)² + (AB)·(CD) represents the Pythagorean theorem, which is a fundamental concept in geometry stating that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This equation is only applicable to right triangles and has many practical applications in fields such as architecture, engineering, and navigation. There are various methods to prove the Pythagorean theorem, including geometric proofs and algebraic manipulation. Real-world examples of its use include calculating diagonal lengths, determining building heights, and navigation.
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Albert1
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FAQ: Prove: (AC)² = (AD)² + (AB)·(CD)
What does the equation (AC)² = (AD)² + (AB)·(CD) represent?
The equation represents the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the lengths of the other two sides (AD) and (AB)·(CD).
Is this equation applicable to all triangles?
No, this equation is only applicable to right triangles, which are triangles with one 90 degree angle.
Why is the Pythagorean theorem important?
The Pythagorean theorem is important because it is a fundamental concept in geometry and has many practical applications in fields such as architecture, engineering, and navigation. It also allows us to calculate distances and solve real-world problems involving right triangles.
How do you prove that (AC)² = (AD)² + (AB)·(CD)?
There are several ways to prove the Pythagorean theorem, one of which is through a geometric proof using similar triangles. Another method is using algebraic manipulation and the concept of the distance formula. Ultimately, the proof relies on the relationship between the sides of a right triangle and the properties of squares and square roots.
What are some real-world examples where the Pythagorean theorem is used?
The Pythagorean theorem is used in various fields, such as construction, carpentry, and surveying. For instance, it is used to calculate the diagonal length of a TV screen or computer monitor, to determine the height of a building using a measuring tape, and to create diagonal lines in carpentry projects. It is also used in navigation to determine distances between points on a map.