Download - Let’s get started .
Let’s get started . . .
Raise your hand if you can identify the family:
20
12
16 78
30
7268
32
60
(3, 4, 5)*4 (5, 12, 13)*6 (8, 15, 17)*4
175
49
168
(7, 24, 25)*7
AppetizersWhat do you notice about these triangles?
60
30
7
1437
60
30
10
20310
60
30
173
3463173
45
45
7
7
27
45
45
25
25
225
45
45
9
9
29
Section 7-3Special Right Triangles
By the end of this lesson you will be able to*identify the ratio of the side lengths of a 30-60-90 *identify the ratio of the side lengths of a 45-45-90
Theorem: In a triangle whose angles have the measures 30, 60, and 90, the lengths of the sides opposite these angles can be represented by x, , and 2x respectively. (30-60-90-Triangle Theorem)
Formally . . .
3x
The side opposite the 30 angle (the shorter leg) is one-half the hypotenuse. The side opposite the 60 angle (longer leg) is
times the shorter leg.
Informally . . .
3
Say what???????
60
30
3x
x
2x
Theorem: In a triangle whose angles have the measures 45, 45, and 90, the lengths of the sides opposite these angles can be represented by x, x, and respectively. (45-45-90-Triangle Theorem)
Formally . . .
2x
The hypotenuse is times the leg.
Informally . . .
2
Say what???????
45
2x
45
x
x
Six Common Families of
Right Triangles
(3, 4, 5)(5, 12, 13)
(30-60-90)(7, 24, 25)
(45-45-90)(8, 15, 17)
4 + 2 makes = 6 Right Families
2x) 3 x(x, ,
)2 x x,(x,
Apply it . . .
Find the perimeter of isosceles trapezoid EFGH.
60
E 10
16
H
F G
Find the perimeter of isosceles trapezoid JMOP.
45
P 8
6
O
J M
P=38
21228P
Angling Your Way . . .
Raise your hand if you can identify the missing angles, starting with the smaller:
60
3035
10
5
A
BC
It’s Nice to be Special . . .
Raise your hand if you can find the missing side:
445
45
22
22
Missing . . .
Raise your hand if you can find the missing sides, starting with the leg:
38
60
816
Show Some Leg(s) . . .
Raise your hand if you can find the missing side(s):
25
45
45
10
25
Same but Different . . .
Raise your hand if you can find the missing side:
45 45
7
27
7
More . . .
Raise your hand if you can find the missing sides, starting with the leg:
338
30
8
3316
Even More . . .
Raise your hand if you can find the missing sides, starting with the leg:
3310
30
10
3320
Almost Done . . .Raise your hand if you can find the missing sides, starting with the leg:
320
60
20
40
Grand Finale
Raise your hand if you can find the side(s) of this equilateral triangle:
35
3015
310
