7.3 Special Right Triangles

1
7.3 Special Right Triangles

• Chapter 7 Area

2
Find the Hypotenuse, leave your answer in
simplest radical form.
4
3
3
4
2
What do you notice?
2
3
45-45-90 Triangles (Isosceles Right Triangles)

• The Legs are congruent
• The Hypotenuse is the leg
• times the v2

xv2
x
x
4
45-45-90 Triangles (Isosceles Right Triangles)
5
5
5
45-45-90 Triangles
If you are given the hypotenuse and Must find the
leg, DIVIDE by v2
10v2
6
45-45-90 Triangles
If you are given the hypotenuse and Must find the
leg, DIVIDE by v2
20
7
To Recap 45-45-90 Triangles

• Leg to Hypotenuse Multiply by v2
• Hypotenuse to Leg Divide by v2
• The Legs are always Congruent

xv2
x
x
8
Equilateral Triangles

• In an Equilateral Triangle, all sides and angles
  are congruent. Therefore, each angle is 60.

60
60
60
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Equilateral Triangles

• If we cut it in half, what happens?

Using Pythagorean Theorem, solve for the height
of the triangle in simplest radical form.
30
30
10
10
5v3
60
60
5
10
30-60-90 Triangles

• Long Leg is across from the 60 angle
• Short Leg is across from the 30 angle
• Hypotenuse is across from the right angle

30
Hypotenuse
Long Leg
60
Short Leg
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30-60-90 Triangles

• Short Leg is always your starting point
• Long Leg is v3 times the Short Leg
• Hypotenuse is 2 times the Short Leg

30
Hypotenuse 2x
Long Leg xv3
60
Short Leg x
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30-60-90 Triangles

• Short Leg to Hypotenuse Multiply by 2
• Hypotenuse to Short Leg Divide by 2
• Short Leg to Long Leg Multiply by v3
• Long Leg to Short Leg Divide by v3

30
Hypotenuse 2x
Long Leg xv3
60
Short Leg x
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30-60-90 Triangles
4
30
60
12
30
60
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30-60-90 Triangles
30
60
6v3
15
15
Practice

• Pg 369 1-29