discovering geometry chapter 9...dec 04, 2013 · pythagorean practice solve the following using...
TRANSCRIPT
Discovering
Geometry
Chapter 9
Lesson 1: 9.1, 9.2, 9.5
Lesson 2: 9.3
Lesson 3: 9.4
WARM-UP
Draw a scalene right triangle
Label the parts you remember.
Measure the sides.
SECTIONS 9-1, 9-2 AND 9-5:
THE PYTHAGOREAN THEOREM AND DISTANCE
In these sections we will answer…
Why is it so important to be right?
What is the Pythagorean Theorem?
How can I tell a right triangle from a wrong one?
How can I use Pythagorean Theorem to solve real life
problems?
How can I determine distance on the coordinate
plane?
PYTHAGOREAN THEOREM
a2 + b2 = c2
where a and b are legs and
c is the hypotenuse or longest
side
***Pythagorean Theorem only
works on RIGHT TRIANGLES!
Pythagorean Practice
Solve the following using the
Pythagorean Theorem:
1. Find c if a = 3 and b = 4.
2. Find c if a = 12 and b= 5.
3. Find b if a = 4 and c = 8
4. Find a if b = 6 and c = 9.
5. Find b if a = 15 and c = 18.
A
b
a
c
C B
2 2 2a b c
ANSWERS:
1. c = 5
2. c = 13
3. c = 6.9 or 4
4. a = 6.7 or 3
5. b = 9.9 or 3
3
5
11
How can you tell if a triangle is right using
the Pythagorean Theorem?
Right: c2 = a2 + b2
Obtuse: c2 > a2 + b2
Acute: c2 < a2 + b2
ARE THESE RIGHT TRIANGLES? IF NOT, IS
IT OBTUSE OR ACUTE?
USING THE PYTHAGOREAN THEOREM
TO SOLVE PROBLEMS:
USING THE PYTHAGOREAN THEOREM
TO SOLVE PROBLEMS:
A rectangular garden 6 meters wide has a diagonal
measuring 10 meters. Find the perimeter of the garden.
USING THE PYTHAGOREAN THEOREM
TO SOLVE PROBLEMS:
How high up on the wall will a 20-foot ladder touch if
the foot of the ladder is placed 5 feet from the wall?
USING THE PYTHAGOREAN THEOREM TO FIND
DISTANCE ON THE COORDINATE PLANE:
THE DISTANCE FORMULA:
1 1 2 2The distance between points ( , ) and ( , ) is given by
2 2 1 12 2
( ) ( )
A x y B x y
AB x x y y
FIND THE DISTANCE BETWEEN THE POINTS:
USING THE DISTANCE FORMULA TO SOLVE
PROBLEMS
Find the perimeter of ∆ABC with vertices A(2 , 4),
B(8 , 12), and C(24 , 0).
SIDE LENGTH
SIDE SLOPE DISTANCE
AB
BC
CD
DA
HOMEWORK
Worksheet 9-1, 9-2, 9-5 (front and back)