Geometry

1
Geometry

• Lesson 9-3

2
Special Right Triangles

• What makes a special right triangle is the
  triangles angles.
• One of those special right triangles is a 45? -
  45? - 90? triangle.
• Theorem 9-5 - In a 45? 45? 90? triangle,
  the hypotenuse is times as long as a leg.
• Hypotenuse leg ?
• (hyp leg? )

3
Example

• Find c using Pythagorean Theorem.
• 52 52 c2
  5 c
• 25 25 c2
• 50 c2
• c2

c
5
5
4
Example using 45 45 - 90

• Ex. Find the value of x. Simplify the radical
  if possible.

x
7
45?
5
Example using 45 45 90

• Find the value of x. Simplify the radical if
  possible.

5
x
5
5
5
6
More Special Right Triangles

• There is another right triangle whose angles
  allow us to use formulas to find the length of a
  side. 30-60-90 triangles.

30?
long leg (ll)
Hypotenuse (hyp)
60?
90?
short leg (sl)
7
Theorem 9-6

• In a 30-60-90 triangle ,the hypotenuse is
  twice as long as the shorter leg, and the longer
  leg is times as long as the shorter leg.
  (30? - 60? - 90? theorem)
• hyp. short leg ? 2 (hyp sl ? 2)
• Long leg short leg ? ( ll sl )

8
Example

• Find the values of x and y.
• 
  
  Ans. x 10, y 5

x
y
60?
5
9
Example

• Find the values of x and y.
• 
  
  Ans. x 6, y 6

12
x
30?
y
10
Example

• Find the value of x and y.
• 
  Ans. x , y

y
5
60?
x
11
Assignment

• Worksheet 1-18 all