Exploring Special Right Triangles in Geometry

The video tutorial covers special right triangles, focusing on 45-45-90 and 30-60-90 triangles. It explains the properties and calculations for each type, including how to find unknown sides using radicals. The 45-45-90 triangle is isosceles, with equal legs and a hypotenuse calculated by multiplying a leg by radical two. The 30-60-90 triangle has different angles, with the hypotenuse twice the smaller leg and the longer leg calculated by multiplying the smaller leg by radical three.

What is the length of the hypotenuse in a 45-45-90 triangle if one leg is 5?

• 7.5

• 5 radical 3

• 10

• 5 radical 2

In a 45-45-90 triangle, if the hypotenuse is 7, what is the length of one leg?

• 7 radical 2 over 2

• 3.5

• 7 radical 3 over 2

• 14

What is the relationship between the legs of a 45-45-90 triangle?

• They are equal in length

• One is twice the length of the other

• They are unrelated

• One is three times the length of the other

How is the hypotenuse related to the legs in a 45-45-90 triangle?

• It is half the length of one leg

• It is the product of one leg and radical 2

• It is the sum of the legs

• It is twice the length of one leg

What is a unique property of the 45-45-90 triangle?

• It has one obtuse angle

• It has no equal sides

• It is a scalene triangle

• It is an isosceles triangle

How do you find the length of the larger leg in a 30-60-90 triangle?

• Multiply the smaller leg by radical 3

• Multiply the smaller leg by radical 2

• Divide the hypotenuse by radical 3

• Divide the hypotenuse by 2

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the smaller leg?

• 6

• 4 radical 3

• 12 radical 3

• 12 radical 2

In a 30-60-90 triangle, if the larger leg is 12, what is the length of the hypotenuse?

• 12 radical 2

• 24

• 8 radical 3

• 6 radical 3

In a 30-60-90 triangle, how do you find the length of the smaller leg if the hypotenuse is given?

• Multiply the hypotenuse by 2

• Divide the hypotenuse by radical 2

• Multiply the hypotenuse by radical 3

• Divide the hypotenuse by 2

If the smaller leg in a 30-60-90 triangle is 4 radical 3, what is the length of the larger leg?

• 16 radical 3

• 8 radical 3

• 24

• 12