Special Right Triangles
Recognizing special right triangles in geometry can help you to answer some questions quicker. A special right-triangle is a right triangle whose sides are in a particular ratio. You can also use the Pythagorean theorem, but if you can see that it is a special triangle it can save you some calculations.
There are two types of special triangles: 45
0-45
0-90
0 triangles and 30
0-60
0-90
0 triangles.
450-450-900 Triangles
A 45
0- 45
0- 90
0 triangle is a special right-triangle whose angles are 45
0, 45
0and 90
0. The lengths of the sides of a 45
0- 45
0- 90
0 triangle are in the ratio of
1: 1:√2.
A right triangle with two sides of equal lengths is a 450- 450- 900 triangle.
Side 1: side 2 : hypotenuse = a : a: a√2
Example 1:
Find x.
Solution:
This is a right triangle with two equal sides so it must be a 45
0- 45
0- 90
0 triangle.
So we use, a : a: a√2
Here a = 6
Hypotenuse = a√2 = 6√2.
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Example 2 : Find the side of an isosceles right triangle if its hypotenuse is 10√2.
Solution:
Isosceles right triangle means 45
0- 45
0- 90
0 triangle.
So we use, a : a: a√2
Here hypotenuse = a√2 = 10√2
Side = a = 10
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Example 3 : Find the side of an isosceles right triangle if its hypotenuse is 18.
Solution:
Isosceles right triangle means 45
0- 45
0- 90
0 triangle.
So we use, a : a: a√2
Here hypotenuse = a√2 = 18
Side = a = 18/√2
a= (18x√2)/(√2x√2) (Rationalize the denominator)
a = 18√2/2
a = 9√2
Each side = 9√2
Special Right Triangles
Special Right Triangles
30-60-90 Triangles
Pythagorean Theorem
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