Pythagorean Theorem Unit Assessment

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 are the conditions for three lengths to form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

If a triangle has sides of lengths 9, 9, and 9, what type of triangle is it?

Back

It is an equilateral triangle, as all three sides are equal.

Front

Can the sides measuring 26 inches, 24 inches, and 5 inches form a triangle?

Back

Yes, these sides can form a triangle because they satisfy the Triangle Inequality Theorem.

Front

What is the formula to find the hypotenuse of a right triangle if the other two sides are known?

Back

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

Front

What is an example of a set of lengths that cannot form a triangle?

Back

The lengths 28, 30, and 58 cannot form a triangle because 28 + 30 is not greater than 58.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various real-life applications, such as construction, navigation, and physics, to calculate distances and ensure structures are built correctly.