Pythagorean Theorem and Pythagorean Inequalities 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: a² + b² = c².

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle measuring more than 90 degrees.

Front

How can you determine if a triangle is right, acute, or obtuse using side lengths?

Back

You can use the Pythagorean Theorem: If a² + b² = c², the triangle is right. If a² + b² > c², it is acute. If a² + b² < c², it is obtuse.

Front

What are the Pythagorean Inequalities?

Back

The Pythagorean Inequalities are rules that help determine the type of triangle based on the lengths of its sides. They state that for any triangle with sides a, b, and c (where c is the longest side): 1) If a² + b² > c², the triangle is acute. 2) If a² + b² = c², the triangle is right. 3) If a² + b² < c², the triangle is obtuse.

Front

Solve for x: x² + 36 = 100

Back

x = 8 or x = -8 (only x = 8 is valid in this context).

Front

Solve for x: 2x² = 72

Back

x = 6 or x = -6 (only x = 6 is valid in this context).

Front

Do the lengths 7, 9, and 13 form a right triangle?

Back

No, they form an obtuse triangle.

Front

Do the lengths 6, 8, and 10 form a right triangle?

Back

Yes, they form a right triangle.