Special Right Triangles

Name Computer Number

I. Construct an isosceles right triangle ABC, where AC is the hypotenuse. Measure the legs and the hypotenuse to the nearest tenth.

AB =

BC =

AC =

Divide: Hypotenuse/Leg = This ratio is equal to the square root of what integer?

1) If AB = 2, then AC = and BC =

2) If AC = 6, then AB = and BC =

3) If AB = x, then AC = and BC =

What is the special formula used for 45-45-90 triangles?

Using this formula, work out numbers 1 and 2 below and leave answers in simplified radical form.

1) AC = BC =

2) AB = BC =

II. Construct a 30-60-90 triangle XYZ, where XZ is the hypotenuse,

XY =

YZ =

XZ =

XY is called the leg and YZ is called the leg.

Which leg could you double to get the hypotenuse?

Divide: Long leg/ Short Leg = This ratio is equal to the square root of what integer?

1) If XZ = 10, then XY = and YZ =

2) If the short leg = 8, then XY = and XZ =

3) If the long leg = 6, then XZ = and YZ =

What are the special formulas used for 30-60-90 triangles?

III. Using these formulas, work out numbers 1, 2, and 3. Place answers in decimal form AND simplified radical form.

1)
 Decimal Form Radical Form XY YZ

2)

 Decimal Form Radical Form XY XZ

3)

 Decimal Form Radical Form XZ YZ