Identifying Triangles by Hypotenuse Length

Front

What is a hypotenuse?

Back

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

Front

In a right triangle, if one leg is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean theorem: a² + b² = c², where c is the hypotenuse.)

Tags

CCSS.8.G.B.8

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): c² = a² + b².

Tags

CCSS.8.G.B.7

Front

If the hypotenuse of a right triangle is 10, and one leg is 6, what is the length of the other leg?

Back

8 (Using the Pythagorean theorem: 10² = 6² + b², so b = 8.)

Tags

CCSS.8.G.B.7

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the sides of 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

How do you identify a right triangle?

Back

A right triangle can be identified by the presence of a 90-degree angle.

Tags

CCSS.2.G.A.1

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, it is a right triangle because 5² + 12² = 13².

Tags

CCSS.8.G.B.8

Front

What is the formula to find the hypotenuse in a right triangle?

Back

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

Tags

CCSS.8.G.B.8

Front

What is the length of the hypotenuse if both legs of a right triangle are equal to 1?

Back

√2 (Using the Pythagorean theorem: 1² + 1² = c², so c = √2.)

Tags

CCSS.8.G.B.8