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). Formula: a² + b² = c².

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.

5 cm (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

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

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Yes, it is a right triangle (5² + 12² = 25 + 144 = 169; √169 = 13).

Area = (1/2) × base × height.

The corresponding sides of similar triangles are in proportion.

If in a triangle, the square of the length of one side is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.