Warm up Session 14

1
Warm up Session 14

• Angle 1 is complementary to Angle 4. Angle 1 is
  62. What is the measure of Angle 4?
• P is the midpoint of segment AB. Find AB if PB
  82
• Similar triangles are _____ congruent (always,
  sometimes, never)
• Can you prove these congruent? If so, what
  theorem?
• (Brain teaser) often not often not often

28? 164
_______ SSS More often than not
2
Agenda
Tues, March 24 Quiz 9.1-9.3

• Warm-Up
• Notes 9.2
• Pythagorean Theorem
• Notes 9.3
• Converse of the Pyth. THM
• Worksheets 9.2 9.3
• Hand back tests

Wed, March 25 Section 9.4 Special Rt tri
Thur, March 26 Section 9.5 Trig
How can you tell if a triangle is acute, obtuse,
or right just by looking at the sides?
3
Review of Radicals
Factor Tree
Simplify
Find all prime factors
4
EX1 Simplify.
When you have a pair, bring the number out.
Prime Factor
45
3
15
3
5
5
EX2 Simplify
When you have a pair, bring the number out.
Prime Factor
48
2
24
2
12
2
6
2
3
6
EX3 Simplify.
When you have a pair, bring the number out.
Prime Factor
45
3
15
3
5
7
REVIEW
LEG
HYPOTENUSE
LEG
8
Pythagorean Theorem
c
a
b
The square of the hypotenuse is equal to the sum
of the square of the other two sides.
ONLY FOR RIGHT TRIANGLES
9
10 Minute Pythagoras Movie Clip

• What is the shortest distance between two points?
• How long should the ladder be to reach the top of
  the castle wall?
• How far out (in yards) should Eliza Dickson tack
  down the guy wire?
• Where is Pythagoras from?
• Who had clay tablets of triples 1200 years before
  Pythagoras?
• How many Books are in Euclids Elements?

10
Other Interesting Facts??
Pythagoras (569-500 B.C.) was
born on the island of Samos in Greece.
11
Picture of the statue Pythagoras in the island
of Samos
Other Interesting Facts??
12
Other Interesting Facts??
Leonardo da Vinci discovered his own proof of the
Pythagorean Theorem.
13
The twentieth president of the United States,
James A. Garfield, discovered a proof to the
Pythagorean Theorem five years before he become
President. He discovered the proof in 1876 during
a mathematics discussion with some of the members
of Congress.
Other Interesting Facts??
14
Interesting Facts??
Babylonians had clay tablets of rules for
creating Pythagorean triples 1200 years before
Pythagoras was around.
15
Ex 4 Solve for x
x
4
3
3, 4, 5 is a PYTHAGOREAN TRIPLE
16
Ex 5 Solve for x
10
8
x
8, 6, 10 is a PYTHAGOREAN TRIPLE
17
A PYTHAGOREAN TRIPLE is a set of three integers
that makes the Pythagorean theorem true.
Can you think of another Pythagorean triple?
18
Any multiple of 3, 4, 5
Any multiple of 5, 12, 13
6, 8, 10 9, 12, 15 12, 16, 20
10, 24, 26 15, 36, 39 20, 48, 52
Most Common Pythagorean Triples
19
How can you tell if it is possible for three
sides to form a triangle?
The 2 smaller sides must add up to be MORE THAN
the largest side.
20
Ex. 6 Determine if the three numbers can be
measures of the sides of a triangle. If no,
explain.

• 13, 28, 19
• 28, 96, 124

Yes
Yes
NO
21
How can you tell if a triangle is Obtuse, Right
or Acute using the Pythagorean Theorem?
22
We must look at the relationship between the
sides. C is the largest side.
gt
lt

gt
OBTUSE
lt
ACUTE

RIGHT
23
Ex. 7 Classify the triangles with the given side
lengths as right, acute, or obtuse.
121 ? 49 81

• 7, 9, 11
• 6, 6, 10
• c.

ACUTE
121 lt 130
100 ? 36 36
OBTUSE
100 gt 72
54 ? 5 49
RIGHT
54 54
24
Let's Practice! Worksheet 9.2 B 1 - 17 (omit
16) Worksheet 9.3 B 1 - 12
25
HW Worksheet Extra Practice 9.2 13 - 18
Worksheet Extra Practice 9.3 1 - 16
26
What you should have learned today
What is the Pythagorean Theorem?
What side does the variable c represent?
How would you classify a triangle with
.
In a right triangle, what is the relationship
between and .