warm up for section 1.1 (tuesday, august 7) simplify: (1). (2). find the two missing edge lengths in...
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Warm Up for Section 1.1 (Tuesday, August 7)
Simplify: (1). (2).
Find the two missing edge lengths in each triangle:
(3). (4). (5).
5032
6
45o
7
45o
34
8
Warm Up for Section 1.1 (Tuesday, August 7)
Simplify: (1). (2).
Find the two missing edge lengths in each triangle:
(3). (4). (5).
5032
6
45o
7
45o
34
8
21523
7 273464
24
24
Work for Answers to WU, Section 1.1
(1). (2).
215
253
2253
2253503
232
26
26
26
22
Special Right Triangles Section 1.1
Day 2
Essential Question: What is the relationship between the lengths of the edges in a 30°–60°–90° triangle?
Standard: MM2G1a, b
Investigation 2:
With your partner, complete the following regarding equilateral ABC where AB =10:
Step 1: Label the length of each edge.Step 2: Label the measure of B and C.Step 3: Using a straightedge, draw and label altitude . Step 4: Label the length of and .Step 5: Label the measure of BAD and CAD.Step 6: Label the measure of ADC.Step 7: Using the Pythagorean Theorem, find AD.
AD
CD BD
10
10
10
5 5
60°
30°
60°
a2 + b2 = c2
52 + x2 = 102
25 + x2 = 10075 = x2
x75
x35
30°
A
BC D
x
x 325
Investigation 2:
Note: the two legs of a 30o-60o-90o triangle are NOT equal in measure. The longer leg will always be opposite the ___o
angle.
The shorter leg will always be opposite the ___o angle.
60
30
Consider the 30o-60o-90o right triangle created from an equilateral triangle pictured at right. (2). The long leg is segment ______
and the short leg is segment _______.
(3). Use the Pythagorean Theorem to find RT.
RT
ST12
6
60°
30°
x
R
TS
12
6
60°
30°
a2 + b2 = c2
62 + x2 = 122
36 + x2 = 144108 = x2
x108
x36x
R
TS
x 336
2x
x
60°
30°
3x
Length of hypotenuse = length of short leg times 2
Length of long leg: length of short leg times
Length of short leg: half the length of hypotenuse or the length of the long leg divided by
3
3
Summary: In a 30o-60o-90o triangle:
Check for Understanding: Find the missing edge lengths for each triangle:
Example 4:
26
x
x2x
226 x
226 x22
x66
6
Check for Understanding: Find the missing edge lengths for each triangle:
Example 5:
60o
30o
3834 x x2
3x
382 x
22
34x
382 x
12
34
3)34(3
x
12
Check for Understanding: Find the missing edge lengths for each triangle:
Example 6:
5
5
10
x
x
2x
5x
10
252
x
Check for Understanding: Find the missing edge lengths for each triangle:
Example 7:
4
34
8
x
3x
x2
4x
8)4(22
343
x
x
60o
30o
Check for Understanding: Find the missing edge lengths for each triangle:
Example 8:
37
7x
3x x2
14)7(22
7
3
37
3
3
373
x
x
x
x
60o
30o
14
Check for Understanding: Find the missing edge lengths for each triangle:
Example 9:
24
312
x
3x
x2
3123
122
24
2
2
242
x
x
x
x60o
30o
12
Application problems: (7). Find the exact area of an equilateral triangle whose edge length is 12 cm. Round your answer to the nearest tenth. Recall: A = ½bh.
12
12
12
6 6
h60o60o
60o
A = ½bhA = ½(12)A =A ≈ 62.4 cm2
)36(336
Application problems: (8). Find the exact perimeter of square ABDC if FB = 22 meters
P = 4sP = 4P =
)222(
2
44s
A
F
B
C D
22
22
2
2
2
244 222
meters28845o
45o
60°
30°Formula Sheet:
Length of long leg = length short leg ∙ _____Length of hypotenuse = length short leg ∙ _____Length of short leg = length long leg ÷ ______Length of short leg = length hypotenuse ÷ ______
x
3xx2
3
23
2
Pythagorean Theorem:
a2 + b2 = c2
72 + x2 = 102 49 + x2 = 100 x2 = 51 x = 51
7
10 x
Triangle Sum Property:
Sum of interior s = _____180
25°
30°x°
x = 180o – 25o – 30o = 125o
Linear Pair:
x = 180o – 120o = 60o
120°x°