Special Right Triangles

1
Special Right Triangles
2
45-45-90Right Isosceles Triangle
Leg


Leg
Hypotenuse
Legs are congruent Hypotenuse Legs
3
45-45-90Right Isosceles Triangle
s






Leg
Hyp
Leg
1
1
s
3
3
2
12
4
45-45-90Right 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 ? 26 ? 2 72
1- Perimeter 28 4x 28 x 7 Leg
7 Hyp 7 ? 2
5
30-60-90
Short Leg
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
30-60-90
ShortLeg Long Leg Hyp






x
1
2

3
6
2x
4
2
6
12
12
24
12
7
30-60-90
When you draw the altitude of an equilateral
triangle, you create two 30-60-90 triangles. The
triangle side length is the hypotenuse of the
30-60-90. Half of the side length is the short
leg of the 30-60-90. The altitude, then, is half
the triangle side times the square root of 3.
60


2x
30
30
60
60


x
2x