Geometry

1
Geometry

• 8.2 The Pythagorean Theorem
• (This section, along with 8.4, are very important
  as they are utilized throughout the second
  semester)

2
Radical Review

• Simplify each expression.

8/3
5
You try!
28
9/5
3
Do you know these?
2
2
14
196
7
49
2
8
64
2
13
169
2
2
15
225
9
81
2
12
2
144
10
100
2
16
256
2
11
2
121
17
289
4
Pythagorean Theorem

• In a right triangle, the square of the hypotenuse
  is equal to the sum of the squares of the legs.

A
c
b
a
C
B
5
Pythagorean Theorem Proof
This is in the state standards and may be on the
STAR test!
c
Area of large square Area of large square
c
½ ab
a
a
large square
4 triangles small square
b
½ ab
(b a)
2
2
2
c
4(½ ab)
(b 2ab a )
c

(b a)
b
c
c
2
2
b 2ab a
b
2
2
2
c
c

2ab
b 2ab a
(b a)
½ ab
(b a)
2
2
2
c

b a
a
b
2
2
2
c
½ ab

a b
a
c
c
(b a)(b a)
2
2
b 2ab a
6
Find the value of x together.
B

BC
AC
AB
x
1)
8
6
x 10
15
2)
x
9
x 12
A
C
7)
12
x
x
7
Find the value of x on your own.
Who can solve these on the board?
B

BC
AC
AB
x
x
3)
5
5
4)
x
3
x
6
5)
x
1
x 1
A
C
2
6)
1
x
x
12
8)
x
8
x
8
Reminders

• The diagonals of a rhombus are perpendicular to
  each other.
• The altitude drawn to the base of an isosceles
  triangle is perpendicular to the base at its
  midpoint.

9
Solve for x.
9)
2
2
2
3 6 x
2
9 36 x
6
2
45 x
9 5
3 3
10
Solve for x.
16)
y
2
2
2
15 y 17
2
225 y 289
2
y 64
y 8
2
2
2
6 8 x
You may recognize this one, x 10.
11
18) The diagonals of a rhombus have lengths 18
and 24. Find the perimeter of the rhombus.
A rhombus has perpendicular diagonals.
2
2
2
9 12 x
x
15
15
12
2
81 144 x
2
225 x
9
x 15
15
15
Thus, the perimeter is 60.
A rhombus is a parallelogram. Diagonals of a
parallelogram bisect each other.
12
Answers to exercises 10-20

• 10) x 17
• 11) x 4
• 12) x 3
• 13) x 8
• 14)
• 15)
• 17)
• 19)
• 20) x 7, so 2(7) is 14

13
HOMEWORK

• pg. 292 1-29 odd