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). It can be expressed as: 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 6 and the other side is 8, what is the length of the hypotenuse?

Back

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

Front

What is the formula to find the length of a side in a right triangle using the Pythagorean Theorem?

Back

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

Front

In a triangle, if one side is 5 and the hypotenuse is 13, what is the length of the other side?

Back

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

Front

What does it mean for two triangles to be similar?

Back

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

Front

If a triangle has sides of lengths 9, 12, and 15, is it a right triangle?

Back

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

Front

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

Back

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

Front

If a triangle has sides of lengths 8, 15, and 17, what type of triangle is it?

Back

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

Front

How do you find the length of a side using the Side Splitter Theorem?

Back

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.