1. Special Right Triangles

2. 45-45-90 Right Isosceles Triangle
Leg
Leg
Hypotenuse
Legs are congruent
Hypotenuse =
Legs =

3. 45-45-90 Right Isosceles Triangle
Leg
Leg
Hyp 1 1 s 3 3 2 12

4. 45-45-90 Right Isosceles Triangle
Leg
The diagonal of a square is the Hypotenuse of two isosceles right triangles.
Leg
1-If the perimeter of the square is 28, what is the length of the diagonal?
2- If the diagonal has a length of 12, what is the perimeter of the square? Area?
2- Diagonal = 12
Leg = 12÷ 2 = 6  2
P = 4(6  2) =24  2
A = 6  2·6  2 = 72
1- Perimeter = 28
4x = 28
x = 7
Leg = 7
Hyp = 7  2

5. 30-60-90 Know the Short Leg (SL): Hypotenuse = 2 · SL Long Leg =
Know Hypotenuse:
Short leg = ½ Hypotenuse
Know Long Leg (LL):
Short leg =
60°
Long
Leg
Hypotenuse
30°

6.
ShortLeg
Long Leg
Hyp x 1 2 3 6 2x 2 4 6 12 12 24 12

7.
When you draw the altitude of an equilateral triangle, you create two triangles.
The triangle side length is the hypotenuse of the
Half of the side length is the short leg of the
The altitude, then, is half the triangle side times the square root of 3.
60° 2x
30°
30°
60°
60° x 2x