special right triangles chapter 8 section 3 learning goal: use properties of 45°-45 °-90 °, and...
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Special Right Triangles
Chapter 8 Section 3
Learning Goal: Use properties of 45°-45 °-90 °, and
30 °-60 °-90 ° Triangles
We make a living by what we get, but we make a life by what we give. -- Winston
Churchill
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45°-45°-90° Triangles Special Right Triangle
x
x d d2 = x2 + x2
d2 = 2x2Simplify:
√d2 = √ 2x2
d = x√ 2
Three sides of lengths x, x, x√2
What did we learn about
ratios of sides?
Ratio of a 45°-45°-90° triangle is:
1 : 1 : √2
45°
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45°-45°-90° Triangles
Find the missing side
a = 4√2 cm
6√245°
6
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45°-45°-90° Triangles
38
45°21
14
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Special Right TrianglesWALLPAPER TILING The wallpaper in the figure can be divided into four equal square quadrants so that each square contains 8 triangles. What is the area of one of the squares if the hypotenuse of each 45°–45°–90° triangle measures millimeters?
A = 24.5 mm
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30°-60°-90° TrianglesConsider an equilateral ∆
2x
x
2x
x
a
60° 60°
30°
a2 = (2x)2 – x2
Simplify: a2 = 4x2 – x2
a2 = 3x2
√a2 = √3x2
a = x√3Three sides of lengths x, 2x, x√3
Ratios of sides?
Ratio of a 30°-60°-90° triangle is:
1 : √3 : 2
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30°-60°-90° Triangles
Find the missing sides
60°
30°5
10
5√3
8√33
4
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30°-60°-90° Triangles
68
30°
4√2
60°
60°
Find the Altitude of the Δ
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Special Right Triangles
Refer to the figure. Find x and y.
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Special Right Triangles
60 cm
The length of the diagonal of a square is cm. Find the perimeter of the square.
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Special Right Triangles
The side of an equilateral triangle measures 21 inches. Find the length of an altitude of the triangle.
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Homework
Special Right Triangles 45-45-90, 30-60-90