45-45-90 Triangles

Front

What is a 45-45-90 triangle?

Back

A 45-45-90 triangle is an isosceles right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees.

Front

What is the relationship between the legs and the hypotenuse in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

If the leg of a 45-45-90 triangle is 5 cm, what is the length of the hypotenuse?

Back

5√2 cm.

Front

What is the formula to find the hypotenuse in a 45-45-90 triangle?

Back

Hypotenuse = leg × √2.

Front

How do you determine if a triangle is acute, right, or obtuse?

Back

A triangle is acute if all angles are less than 90°, right if one angle is exactly 90°, and obtuse if one angle is greater than 90°.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).

Front

If the hypotenuse of a 45-45-90 triangle is 10 cm, what is the length of each leg?

Back

Each leg is 10/√2 or 5√2 cm.

Front

What is the area of a 45-45-90 triangle with legs of length 6 cm?

Back

Area = (1/2) × leg × leg = (1/2) × 6 × 6 = 18 cm².

Front

What is the perimeter of a 45-45-90 triangle with legs of length 3 cm?

Back

Perimeter = leg + leg + hypotenuse = 3 + 3 + 3√2 = 6 + 3√2 cm.

Front

How can you find the length of a leg if the hypotenuse is known in a 45-45-90 triangle?

Back

Leg = hypotenuse / √2.