Pythagorean Theorem

Front

Do the segment lengths 9, 12, and 15 form a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

What is the side of a right triangle across from the right angle called?

Back

Hypotenuse.

Front

If the given side lengths form a triangle, then classify the triangle as acute, right, or obtuse: 6, 9, 15.

Back

Obtuse, because 6² + 9² < 15² (36 + 81 < 225).

Front

Is this a right triangle with sides 8, 10, and 12?

Back

No, because 8² + 10² ≠ 12² (64 + 100 ≠ 144).

Front

If the given side lengths form a triangle, then classify the triangle as acute, right, or obtuse: 10, 12, 15.

Back

Acute, because 10² + 12² > 15² (100 + 144 > 225).

Front

What is the Pythagorean Theorem?

Back

a² + b² = c², where c is the hypotenuse.

Front

If a right triangle has legs of length 3 and 4, what is the length of the hypotenuse?

Back

5, because 3² + 4² = 5² (9 + 16 = 25).

Front

Can the lengths 5, 12, and 13 form a right triangle?

Back

Yes, because 5² + 12² = 13² (25 + 144 = 169).

Front

What type of triangle is formed by sides 7, 24, and 25?

Back

Right triangle, because 7² + 24² = 25² (49 + 576 = 625).

Front

If a triangle has sides of lengths 8, 15, and 17, classify it.

Back

Right triangle, because 8² + 15² = 17² (64 + 225 = 289).