Pythagorean Theorem-STAAR

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: 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 the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If a = 3 and b = 4, what is c?

Back

Using the Pythagorean Theorem: c² = a² + b²; c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

What does it mean for a triangle to be a right triangle?

Back

A triangle is a right triangle if it satisfies the Pythagorean Theorem, meaning the square of the hypotenuse equals the sum of the squares of the other two sides.

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

You can use the Pythagorean Theorem: If a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the sides satisfy the Pythagorean Theorem: 3² + 4² = 5² (9 + 16 = 25). It is a common example of a right triangle.

Front

What is the formula to find the length of one side of a right triangle?

Back

To find the length of one side, rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²).

Front

What does 'further' mean in the context of geometry?

Back

In geometry, 'further' often refers to a greater distance or extent in measurement or analysis.

Front

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

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.