Geometry
8.4 Special Right Triangles
This is a very important section, as it is used
extensively throughout the second semester.
All you need to know is how to
multiply by root two and divide by
root two.
45-45-90 Triangles
The formula.
o
45
x 2
x
o
45
x
Since all 45-45-90 triangles are similar, by AA Similarity Postulate,
this formula works for all 45-45-90 triangles.
Does it work for the Pythagorean Theorem?
 ?
x x  x 2
2
2
2
x
2
x
x 2
o
2
2x = 2x ?
Yes!
45
o
45
x 2
The Two Types of 45-45-90 Problems
Type 1: Given the length of a leg, solve for the other leg and hypotenuse.
3
o
45
What are the other two lengths?
6 2
3
12
o
3 2
45
45o
Multiply by root 2.
6
2 3
o
45
What are the other two lengths?
6
Multiply by root 2.
The Two Types of 45-45-90 Problems
Type 2: Given the length of the hypotenuse, solve for the two legs.
7
2
2
What are the other two lengths?
Shortcut:
o
Divide the length of the hypotenuse
by 2 and multiply by 2 to find the length
of the leg.
45
Divide by root 2.
7
2
2
7
Divide by root 2.
o
45
4 6
45o
8 3
o
45
What are the other two lengths?
4 6
I. 45-45-90
Solve
A
45
leg 2
leg
1.
leg
leg
leg 2
AB
BC
AC
10
2.
45
B
leg
6
C
3.
16
4.
8
5.
6.
10 2
6
Let’s Try Some From the HW
P. 302 #18, 26
 P. 288 #28

HW
P. 302 (1-8, 17, 18, 23, 26, 27)
 P. 288 #27-30




Quiz on Thursday
Please sign up for School Loops(there is a link on my webpage)
Answers to the packet below if you want to work them out:
Day1 P art I
Day I Part III
Day 2 P art III
1)10,10 2
1) x  5 2
1) 5 6 , 5 6
2)3 2 , 3 2
2) x  6 2
2) 3 10, 3 10
3)4, 4 2
4) 4 2 , 4 2
5) 10,10
6) 6, 6 2
3) 3 2 , 6
4) 5 6 , 10 3
Geometry
8.4 Special Right Triangles
Part 2
This is a very important section, as it is used
extensively throughout the second semester.
All you need to know is how to
multiply and divide by two and
multiply and divide by root three.
30-60-90 Triangles
The formula.
o
30
x 3
2x
o
60
x
Since all 30-60-90 triangles are similar, by AA Similarity Postulate,
this formula works for all 30-60-90 triangles.
Does it work for the Pythagorean Theorem?
 
x  x 3  2 x 
2
2
2
x
?
x 2 + 3x 2 = 4x 2 ?
x 2
x 3
Yes!
o
30
o
60
2x
The Three Types of 30-60-90 Problems
Type 1: Given the length of the short leg, solve for the long leg and hypotenuse.
5
Multiply by root 3.
o
60
5 3
Multiply by 2.
10
30o
o
30
3 2
2 6
What are the other two lengths?
Multiply by root 3.
o
60
What are the other two lengths?
6
Multiply by 2.
The Three Types of 30-60-90 Problems
Type 2: Given the length of the hypotenuse, solve for the two legs.
Multiply by root 3.
9
2
What are the other two lengths?
o
60
Divide by 2.
9
3
2
60o
9
3 15
6 5
o
30
Multiply by root 3.
What are the other two lengths?
o
30
3 5
Divide by 2.
The Three Types of 30-60-90 Problems
Type 3: Given the length of the long leg, solve for the short leg and hypotenuse.
3 3
Divide by root 3.
o
Shortcut:
9
60
Multiply by 2
30o
Divide the length of the long leg
by 3 and multiply by 3 to find the length
of the short leg.
o
6 3
30
What are the other two lengths?
5 2
10 6
3
Divide by root 3.
o
60
What are the other two lengths?
5 6
3
Multiply by 2.
II. 30-60-90
Solve:
A
Day 1 Part II
1) 5 3 , 10
8 3 16 3
2)
,
3
3
3) 10 3 , 10
leg 3
leg
AB
BC
2(leg )
AC
30
2(leg)
leg 3
B
60
leg
C
1.
2.
5
8
4) 8 3 , 16
5) 4, 8
3.
20
6) 6 3 , 6
4.
5.
6.
8
4 3
12
III. Solve for x.
1.
2.
x
x
3.
6
10
45
x
x
x
60
45
x
9
Let’s Try A Few From the HW

P. 302 #20, #22
P. 288 #31
HW
P. 302 (9-16)
Quiz Friday
P. 302 (19-25, skip 23)
P. 288 (31,32)
Here are the answers to your packet if you want to work them out.
Day 1 Part II
Day1 Part III
Day 2 P art IV
1) 5 3 , 10
9 3
3) x 
2
1)10 2 , 20 2
8 3 16 3
2)
,
3
3
3) 10 3 , 10
5 6 10 6
,
3
3
3) 6 6 , 12 2
2)
4) 12 15, 24 5
4) 8 3 , 16
5) 3 6 , 3 2
5) 4, 8
7 15 7 5
6)
,
2
2
6) 6 3 , 6