Things to do:

1
Things to do

• Make a new note book
• Get out your homework
• (triangle worksheet)

2
BOE Buried TreasureDay 1

• These notes go with
• Worksheet 1 which is
• Practice 5.4 on one side and
• Practice 12.3 on the other.

3
The Basics

• In a right triangle there are 2 legs and a
  hypotenuse.
• The point where the two legs meet is a right
  angle
• The side across from the right angle is the
  longest side and it is called the hypotenuse.

4
Pythagorean Theorem
a2 b2 c2

• The legs are a and b the hypotenuse is c.

c
a
b
The formula says that if you square the legs and
add them together you will get the length of the
hypotenuse squared.
5
Try this

• Find x

32 42 x2 9 16 x2 25 x2 5 in. x and -5
in. x (x 5 is the answer that will work in
this problem)
52 112 x2 25 121 x2 146 x2 12.08 mi x
and -12.08 mi x (x 12.08 is the answer that
will work in this problem)
x mi.
5 mi.
11 mi.
6
What if we needed the measure of one of the legs

• find x

13 ft.
x
12 ft.
a2 b2 c2 x2 122 132 x2 144 169 x2
25 x 5 ft.
a2 b2 c2 x2 42 152 x2 16 225 x2
209 x 14.46 mi.
7
Pythagorean Inequalities

• when c is the longest side of a triangle you can
  tell if the triangle is acute obtuse or right by
  using the following
• acute c2 lt a2 b2
• obtuse c2 gt a2 b2
• right c2 a2 b2

8
Try this

• Determine whether the triangle is right acute or
  obtuse.

• 32 62 72
• 9 36 49
• 49
• since the hypotenuse is larger than the square of
  the legs it is an obtuse triangle.

1. 7 3 6

lt
2. 14 52 49
142 492 522 196 2401 2704 2597 lt
2704 Obtuse Triangle
9
Just for fun
10

• What is the length of a diagonal of a square with
  side lengths of 10 units
• Step 1 draw it.
• Step 2 label it.
• Step 3 set up an equation
• Step 4 does my answer make sense

x
10
10
10
102 102 x2 100 100 x2 200 x2 14.14 x
10
Try this

• What is the length of a diagonal of a square
  whose side lengths are 5

1. draw it 2. label it 3. set up an
equation 4. solve 5. does the answer make sense
52 52 x2 25 25 x2 50 x2 7.07 x
11
Assignment

• Practice 5.4 (dont do 16)
• Practice 12.3 (all)