Proof PT

Can you easily prove Pythagoras theorem using Euclidean theorems? If so, do it.

Result

Yes

No

Step-by-step explanation:

$$\begin{gathered} a^2=c_a\cdot c \\ {b}^2=c_b\cdot c \\ {a}^2+b^2=c_a\cdot c+c_b\cdot c \\ {a}^2+b^2=c\cdot (c_a+c_b) \\ {a}^2+b^2=c\cdot c \\ {a}^2+b^2=c^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Euclid theorems
  Calculate the sides of a right triangle if leg a = 6 cm, and a section of the hypotenuse, which is located adjacent to the second leg b is 5cm.
• Right 24
  Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 unequal segments. The length of one segment is 5 cm. What is the area of the triangle? Thank you.
• Find radius
  Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r
• Reciprocal
  It is true (prove it) that if a> b> 0: ?
• Short cut
  Imagine that you are going to a friend. That path has a length 120 meters. Then turn doprava and go other 630 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
• Prove
  Prove that k1 and k2 are the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x²+y²+2x+4y+1=0 k2: x²+y²-8x+6y+9=0
• Triangle
  Calculate the triangle sides if its area S = 630 and the second cathetus is shorter by 17.
• Sea
  How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km).
• Medians in right triangle
  It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
• Right isosceles triangle
  Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
• RT - hypotenuse and altitude
  Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
• Truncated cone
  Calculate the height of the rotating truncated cone with volume V = 794 cm³ and a base radii r₁ = 9.9 cm and r₂ = 9.8 cm.
• Square diagonal
  Calculate the length of diagonal of the square with side a = 11 cm.
• Right triangles
  How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).
• Right isosceles triangle
  What can be the area of a right isosceles triangle with a side length of 8 cm?
• Equilateral triangle ABC
  In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont
• Without Euclid laws
  Right triangle ABC with right angle at the C has a=14 and hypotenuse c=26. Calculate the height h of this triangle without the use of Euclidean laws.