Pythagorean Theorem: Explaining A1=A2 & A4=A3

In summary, the Pythagorean Theorem is a mathematical principle stating that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It can be represented by the equation a² + b² = c² and is used in fields such as architecture and physics to calculate distances and angles. It can only be applied to right triangles, with non-right triangles requiring the use of other trigonometric functions.
  • #1
PiRsq
112
0
http://www.ies.co.jp/math/java/geo/pitha1/pitha1-2.gif

This is one of the many pythagorean proofs and I don't understand why A1=A2 and A4=A3? Can someone explain this to me please?
 
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  • #2
ABC, HBA, and HAC are all similar triangles.

That means that the ratio of the sides are the same/
so AB/BC=BH/AB
so AB*AB=BH*BC
so A1=A2

There is a simliar argument for B1 and B2
 
  • #3
I see now, thanks
 

1. What is the Pythagorean Theorem?

The Pythagorean Theorem is a mathematical principle that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

2. How is the Pythagorean Theorem represented mathematically?

The Pythagorean Theorem can be represented using the equation a² + b² = c², where a and b are the lengths of the two shorter sides of the triangle and c is the length of the hypotenuse.

3. What does the A1=A2 and A4=A3 in the Pythagorean Theorem mean?

The A1=A2 and A4=A3 refer to the two smaller squares formed by the sides of the right triangle. A1 and A2 represent the squares of the lengths of the two shorter sides, while A4 and A3 represent the square of the length of the hypotenuse.

4. How is the Pythagorean Theorem used in real-life situations?

The Pythagorean Theorem is used in various fields such as architecture, engineering, and physics. It can be used to calculate distances, heights, and angles in real-life situations involving right triangles.

5. Can the Pythagorean Theorem be used for non-right triangles?

No, the Pythagorean Theorem can only be used for right triangles. For non-right triangles, other trigonometric functions such as sine, cosine, and tangent are used to calculate the sides and angles.

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