Pythagorean Theorem and Side Splitter Theorem

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

The Side Splitter Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

10 (Using the Pythagorean Theorem: 6² + 8² = c², 36 + 64 = c², 100 = c², c = 10).

c = √(a² + b²) where c is the hypotenuse and a and b are the other two sides.

12 (Using the Pythagorean Theorem: 5² + b² = 13², 25 + b² = 169, b² = 144, b = 12).

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Yes, it is a right triangle (9² + 12² = 15², 81 + 144 = 225, 225 = 225).

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

It is a right triangle (8² + 15² = 17², 64 + 225 = 289, 289 = 289).

If a line divides two sides of a triangle proportionally, then the lengths of the segments created on those sides are in the same ratio as the lengths of the other two sides.