Transcript side

Special Right
Triangles, Nets,
Complementary and
Supplementary
Angles, and Dilations
Special Right Triangles
There are two special right triangles!
We will use the Pythagorean Theorem
to discover the relationships between
the sides of the two special triangles.
Isosceles Right Triangle
Conjecture or
45-45-90 Rule
In an isosceles right
triangle, ifs the
legs
have
2
length s, then the
hypotenuse has length
s_______
s 2
Think:
side – side – side 2
s
5 2
Lets try a few: Find the missing sides
1)
52= x
y  52 2
2)
5y
5 2
5 2
5
x
2
52
16
16
x 
2
2 16 2

8 2
2
2
The other special triangle is a
30  60  90 triangle
If you fold an equilateral triangle along one of its altitudes you get a 30-60-90
triangle. Therefore, a 30-60-90 triangle is one half an equilateral triangle so it
appears in math and engineering frequently as well.
Side across
from 30o is the
shortest side,
AIMS reference
calls this side
____
60
Side across from 90o is
the hypotenuse
30
Side across from 60o is
the medium side
30-60-90 Triangle Conjecture
In a 30-60-90 triangle, (easy as 1, 2, 3)
if the shorter side has length s, (think
1s)
then the hypotenuse has length
2s
_____and
the longer leg has length
s 3
______
60
Think:
side – side 3 – 2 · side
s
2s
s 3
30
examples:
4.
5.
y
y  7.5
 24
3
30
12
x
30
x
 12 3
6.
x
10 6
 10 3
15
  7.5
2
7.
8.
 18
y
60
x
10
 36
45
9.
7 3
60
y
x
21
 14 3
x
5 2
Complement and Supplement

complementary angles
A pair of
has a sum of 90°.
1  2  90
B
20°
2
1

A  B  90
70°
A
A pair of supplementary angles
has a sum of 180°. C  D  180
3  4  180
C
30°
4
3
150°
D
Warm-Up: Dilations

Where have you heard the word
“dilate” before?
Eyes – more light, pupils get smaller

What does it mean?
To make wider or larger; cause to expand
1. Dilations
Dilation: A non-rigid transformation in
which the pre-image and the image
are SIMILAR
 Dilations preserve angle measure,
orientation, and collinearity
 Side length changes

Nets
The two-dimensional representation of
all the faces of a 3-dimensional figure
 What a 3-D figure would look like if
you “unfold it”

Types of Nets

Triangular Prism

Square Prism

Square Pyramid

Triangular Pyramid
Types of Triangles