How do you summarize the Pythagorean Theorem?

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

Is the converse of the Pythagorean Theorem true?

The converse of the Pythagorean Theorem is also true. Pythagorean Theorem Converse: If the square 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.

How is Pythagorean theorem used in real life?

Real Life Application of the Pythagoras Theorem The Pythagorean Theorem is useful for two-dimensional navigation. You can use it and two lengths to find the shortest distance. … The distances north and west will be the two legs of the triangle, and the shortest line connecting them will be the diagonal.

Why is the converse of the Pythagorean Theorem important?

The converse of the Pythagorean Theorem enables them to do just this: they can conclude that an angle is a right angle provided a certain relationship holds between side lengths of a triangle.

What is a perpendicular equation?

Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6.

Which is an example of the Pythagorean theorem?

The theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle. Or, the sum of the squares of the two legs of a right triangle is equal to the square of its hypotenuse.

How to do the converse of the Pythagorean theorem?

●Discover the Converse of the Pythagorean Theorem ●Practice working with radical expressions ●Discover relationships among the lengths of the sides of a 45°-45°-90° triangle and among the lengths of the sides of a 30°-60°-90° triangle

How to prove the Pythagorean theorem using differentials?

Proof using differentials. One can arrive at the Pythagorean theorem by studying how changes in a side produce a change in the hypotenuse and employing calculus. The triangle ABC is a right triangle, as shown in the upper part of the diagram, with BC the hypotenuse.

How is the sum of two small squares related to Pythagoras theorem?

Let’s build up squares on the sides of a right triangle. Pythagoras’ Theorem then claims that the sum of (the areas of) two small squares equals (the area of) the large one. In algebraic terms, a2 + b2 = c2 where c is the hypotenuse while a and b are the sides of the triangle.