Special Right Triangles

1
Special Right Triangles
Section 7-3 spi.3.2.G
Jim Smith JCHS
2
Our First Special Right Triangle Is A 3,4,5
The Hypotenuse Must Be A Multiple Of 5 And
The Legs Must Be Multiples Of 3 And 4
3
Use The Pythagorean Theorem To Find X
x
x
3
5
5
3
25 25 x² 50 x² 50 x 5 2 x
9 9 x² 18 x² 18 x 3 2 x
4
Speed Trials 45, 45, 90
7 2
4 2
7
4
4
7
13 2
2 2
2
13
2
13
5
If 2 Sides Of A Triangle Are Congruent, Then The
Angles Opposite Them Are Congruent
45
45, 45, 90

45

6
45, 45, 90
Legs are equal Leg x 2 hyp
45
X 2

X
45

X
Mult by 2
7
Going Backwards.DIVIDE
8
4 2
45
Div by 2
8
30, 60, 90 Triangles
No angles are equal so no sides are congruent
60
Hyp
Short
Leg
30
Long
Leg
9
30, 60, 90 Triangles
Mult by 2
60
Hyp
Short
Leg
30
Long
Leg
10
30, 60, 90
2 x 8 16
60
8
30
11
30, 60, 90
2 x 5 10
60
5
30
12
30, 60, 90
60
Hyp
Short
Leg
30
Long
Leg
Mult by 3
13
30, 60, 90
60
Hyp
15
30
15 x 3 15 3
14
30, 60, 90
60
Hyp
3
30
3 x 3 3 3
15
Going Backwards.DIVIDE
13
60
13 2
H
SL
30
LL
For now, well leave it as an improper fraction
16
Going Backwards.DIVIDE
60
5 3
5
H
SL
3
30
LL
5 3
17
Going Backwards.DIVIDE
8
3
60
H
3
SL
30
LL
8
8
3

3
18
30, 60, 90
12
9
5
30
30
30
6 3
6
19
What Do You Know About This Triangle?
60
30
30


60
60