Geometry
S e c t io n 8 . 3
Name:
D ate :
4 5 - 4 5 - 9 0 S p e c ia l R ig h t T r ia n g le N o t e s : D a y 1
In this lesson you will
find the side lengths of 45-45-90 special right triangles.
Use Pythagorean’s Theorem to find the missing length of each isosceles right triangle. Write all answers in
simplified radical form.
1)
x=
y=
2)
x=
y=
3)
leg =
leg =
4) What pattern do you notice in the relationship between the length of the hypotenuse and the lengths of the legs?
5) In an isosceles right triangle, if the legs have length x, then the hypotenuse has length
.
The formula we will use when solving for missing lengths in a 45-45-90 right triangle is
Example 1:
Example 2:
Example 3:
Example 4:
Example 5: If a square park is cut in half diagonally, what kind of triangle does that make?
Example 6: Below are the lengths of the sides for different triangles. Which are isosceles right triangles?
A)
B)
C)
D)
4, 4 and 7 units each
4, 4 and 4√2 units each
3, 4 and 5 units each
2√3, 2√3 and 2√6 units each
If a square park is cut in half diagonally, what kind of triangle does that
Example 7: Calculate angle y.ample make?
A)
B)
C)
D)
45
35
40
60