Special Right Triangles

Special Right Triangles

Agenda

• ALEKS Warm-Up

• Special Triangles Discovery / Lesson

• Special Triangles Practice

• Mastery Time

Open Ended

If you cut a square in half diagonally, what are the measures of the angles of the 2 triangles created?

Fill in the Blank

Using the Pythagorean Theorem, if you have a 45-45-90 triangle and the two legs are 1 unit, how long is the hypotenuse? (round to nearest hundredth)

Multiple Choice

True or False: All 45-45-90 triangles are similar.

• True

• False

True!

• So, we know that all 45-45-90 triangles are just scaled up or down from lengths of 1, 1, and square root of 2.

Fill in the Blank

If the hypotenuse of a 45-45-90 triangle is

 $3\sqrt{2}$  , what is the length of the leg?

3!

Open Ended

If draw a perpendicular bisector on an equilateral triangle, what are the measures of the angles of the 2 triangles created?

Open Ended

What would the ratio between the short leg and the hypothenuse be? (Think about the side lengths of an equilateral triangle?

Fill in the Blank

Using the Pythagorean Theorem, what would the length of the long side be if the length of the short side was 1 unit, and the length of the hypotenuse is 2 units?

Multiple Choice

True or False: All 30-60-90 triangles are similar.

• True

• False

True!

• So, we know that all 30-60-90 triangles are just scaled up or down from lengths of 1, 2, and

   $\sqrt{3}$  

Fill in the Blank

If the long leg of a 30-60-90 triangle is

 $5\sqrt{3}$  , what is the length of the hypotenuse?