Pythagorean Review

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.

Tags

CCSS.8.G.B.8

Front

What is the formula to calculate the perimeter of a right triangle?

Back

The perimeter (P) of a right triangle can be calculated by adding the lengths of all three sides: P = a + b + c, where a and b are the lengths of the legs and c is the length of the hypotenuse.

Tags

CCSS.3.MD.D.8

Front

If one leg of a right triangle is 9 cm and the hypotenuse is 15 cm, how do you find the other leg?

Back

Use the Pythagorean Theorem: c² = a² + b². Here, 15² = 9² + b². Calculate b² = 15² - 9² = 225 - 81 = 144, so b = √144 = 12 cm.

Tags

CCSS.8.G.B.7

Front

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

Back

In a 3-4-5 triangle, the lengths of the sides are in a ratio of 3:4:5, which satisfies the Pythagorean Theorem. This is a common example of a right triangle.

Tags

CCSS.8.G.B.8

Front

How do you find the height of a ladder leaning against a wall?

Back

Use the Pythagorean Theorem. If the distance from the wall is one leg (a) and the height reached by the ladder is the other leg (b), then the length of the ladder is the hypotenuse (c). Calculate c using c² = a² + b².

Tags

CCSS.8.G.B.8

Front

What is the diagonal of a rectangle with sides 3 feet and 6 feet?

Back

Use the Pythagorean Theorem: d² = 3² + 6². Therefore, d² = 9 + 36 = 45, so d = √45 ≈ 6.7 feet.

Tags

CCSS.8.G.B.7

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 in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What is the significance of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle, and is crucial for applying the Pythagorean Theorem.

Tags

CCSS.8.G.B.8

Front

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

Back

To verify if a triangle with sides a, b, and c (where c is the longest side) is a right triangle, check if a² + b² = c².

Tags

CCSS.8.G.B.8

Front

What is the area of a right triangle?

Back

The area (A) of a right triangle can be calculated using the formula: A = (1/2) * base * height.

Tags

CCSS.6.G.A.1