Pythagorean Theorem and Side Splitter Theorem

Front

What is the Pythagorean Theorem?

Back

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: c² = a² + b².

Front

What is the Side Splitter Theorem?

Back

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.

Front

If one side of a right triangle is 30 cm and the other side is 40 cm, what is the length of the hypotenuse?

Back

50 cm (Using the Pythagorean Theorem: c² = 30² + 40² => c² = 900 + 1600 => c = √2500 = 50).

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

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

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the length of the side opposite the 30° angle is half the length of the hypotenuse, and the length of the side opposite the 60° angle is √3 times the length of the shorter leg.

Front

Find the missing side: a = 12 cm, b = ? cm, c = 13 cm.

Back

5 cm (Using the Pythagorean Theorem: 13² = 12² + b² => 169 = 144 + b² => b² = 25 => b = 5).

Front

If a triangle has sides of lengths 7 cm, 24 cm, and 25 cm, is it a right triangle?

Back

Yes, it is a right triangle (25² = 7² + 24² => 625 = 49 + 576).

Front

What is the formula to find the length of a segment created by a side splitter?

Back

If a line divides two sides of a triangle proportionally, then a/b = c/d, where a and b are segments on one side, and c and d are segments on the other side.

Front

If a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, what type of triangle is it?

Back

It is a right triangle (13² = 5² + 12² => 169 = 25 + 144).

Front

Find the missing side: a = 9 cm, b = 12 cm, c = ? cm.

Back

15 cm (Using the Pythagorean Theorem: c² = 9² + 12² => c² = 81 + 144 => c = √225 = 15).