5.8 Special Right Triangles.notebook
December 02, 2016
45-45-90 Triangles
When given a leg/side
measure (finding the
diagonal or hypotenuse):
When given the diagonal
or hypotenuse (finding a
leg or side measure):
d
d√2
2
d
d√2
2
5.7 Pythagorean Theorem wkst
Dec 16­10:26 AM
1
5.8 Special Right Triangles.notebook
December 02, 2016
What we will learn today:
• To prove and apply the
properties of 45­45­90
triangles.
45-45-90 Triangles
When given a leg/side
measure (finding the
diagonal or hypotenuse):
When given the diagonal
or hypotenuse (finding a
leg or side measure):
d
d√2
2
d
d√2
2
The diagonal of a square
creates two 45­45­90 triangles.
45°
45°
Theorem 8­6
The length of the hypotenuse of a
45°­ 45°­ 90° triangle is √2 times
the length of a leg.
Feb 13­3:37 PM
2
5.8 Special Right Triangles.notebook
December 02, 2016
45­45­90 Triangles
Example 1 ~ Find the value of x in the triangle below.
Example 2 ~ Find the value of x in the triangle below.
Example 3 ~ Find the values of x and y in the triangle
below.
8
Feb 13­3:52 PM
3
5.8 Special Right Triangles.notebook
December 02, 2016
What we will learn today:
• To prove and apply the properties of 30­60­90 triangles.
On your blue notes sheet:
The altitude (height) of an
equilateral triangle creates
two 30­60­90 triangles.
short leg (opposite 30* angle) = s
long leg (opposite 60* angle) = s√3
hypotenuse (opposite right angle) = 2s
Dec 11­8:48 AM
4
5.8 Special Right Triangles.notebook
December 02, 2016
Jan 7­10:57 AM
5
5.8 Special Right Triangles.notebook
December 02, 2016
30­60­90 Triangles
Example 1 ~ Find the values of x and y in the triangle
below.
Example 2 ~ Find the values of x and y in the triangle
below.
Example 3 ~ Find the values of x and y in the triangle
below.
Example 4 ~ Panels in the shape
of equilateral triangles are used
to cover Epcot Center in Disney
World. The side of each tile
measures 4 feet. Find the height
of each panel.
Feb 1­1:36 PM
6