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.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.8.G.B.8

Front

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

Back

5√2 cm.

Tags

CCSS.8.G.B.8

Front

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

Back

Hypotenuse = leg × √2.

Tags

CCSS.8.G.B.8

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°.

Tags

CCSS.4.G.A.2

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).

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.6.G.A.1

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.

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.8.G.B.8