Chapter 5
Example 1
Example 2
Example 3
Example 4
Example 5
Pg 304: 2-4, 12-17
Homework
Name:
Entrance Ticket
Use the map shown and the following information. A town planner is trying to
decide whether a new household X should be covered by fire station A, B, or C.
Draw the segments 𝐴𝐵, 𝐵𝐶, 𝐶𝐴
b. Construct the perpendicular bisectors of 𝐴𝐵, 𝐵𝐶, 𝐶𝐴.
Do the perpendicular bisectors meet at a point?
c. The perpendicular bisectors divide the town into regions.
Shade the region closest to fire station A red. Shade the region
closest to fire station B blue.
Shade the region closest to fire station C yellow.
d. In an emergency at household X, which fire station should respond?
Explain your choice.
Do Now
1) Think: If there were NO bridges where wouldn’t we be able to travel to?
2) What makes up a triangle? What are it’s parts?
There has to be some special relationship between it’s parts …let’s find them!
Grab a ruler and protractor
Discover
Verify: orange +yellow > pink
pink + yellow > orange
Triangle Inequality Theorem
AB + BC > AC
BC+ AC > AB
10cm
7cm
AC + AB > BC
9cm
The sum of the
lengths of ANY
sides of a triangle
must be greater
than the length of
the third side.
Example 1: Is it possible to form a triangle with the
given side lengths? If not, explain why.
a. 8in, 15 in, 17in
b. 6m, 8m, 15m
c. 4 ft, 5ft, 9ft
d. 20 in, 11 in, 15 in
Example 2: Find the range for the measure of the third side of
the triangle given the measure of two sides.
• a. 5m, 11m,
b. 3ft, 7ft,
c. 29km, 7 km,
Practice/Homework
• 5.5 WS
Do Now (next A day quiz)
1)Perpendicular bisectors
2 ) Triangle inequalities( form a triangle or not)
8,3,23
3) What’s the range for the missing side
14, 7,
• 4) Angle-Side Relationships ( compare >, <,=)
EF vs AE
CG vs BC
AB vs BF
Movie Math Fail
• https://www.youtube.com/watch?v=jbvip1Ot6jQ
The sum of the square roots
of two sides of an isosceles
triangle is equal to the square
root of the remaining side
Trivia
• There are over 370 different proofs for the
Pythagorean theorem James Garfield,20th president,
being one of them.
• This dude is Pythagoras. Thank him for this class 
Pythagorean Theorem
•The sum of the squares of 2 legs of a
right triangle is equal to the square of
the hypotenuse.
Examples: 1-3, 4-6
Do Now
• Simplify: (𝑥 + 3)2
Do Now
• In a right triangle a=6 and c =10 solve for b
• Simplify 12211
• Simplify 84
Pythagorean Triples
• https://www.youtube.com/watch?v=rW0wi5-A4z0
Pythagorean Triples
•A set of 3 nonzero whole numbers
that satisfy the Pythagorean
theorem.
•The most common is 3,4,5
Scale Factors of triples
3,4,5
5,12,13
8,15,17
7,24,25
Example 1: Find the missing length of the missing side.
Example 2: Show why the set “6, 8, 10” is a
Pythagorean triple
Applications
Applications
1) Sophia is locked out of her house. The only
open window is on the second floor, which is 12 ft
above the ground. She needs to either grow 7ft or
place a ladder 5 feet from the house to avoid a
bee’s nest. What size ladder does Sophia need?
• 2) Emma and Molly are playing volleyball and
Emma wants to spike the ball right into Molly’s
head. They are 4 feet apart and the ball is 2 feet
in the air above Emma’s head which forms a
right angle. What’s the distance the ball has to
travel to Molly?
26
x
24
What about acute & obtuse triangles?
Is there a relationship??
c
a
c
b
a
b
6
10
8
4
9
.5
.55
.25
5
7
3
15/2
9
45/4
7/2
6
5
10
Examples a-c
Homework- Practice
•Pg 353 15- 29
Do Now
• Pair up with a trustworthy partner
• Choose an egg
• Teach the class your problem
** have your homework out on your desk!!!
Possible Topics: Pythagorean Theorem, Radicals, Inequalities,
Applications, Pythagorean Triples
Ch 5 Recap so far
• Perpendicular bisectors
• Radicals
• Angle-side relationships]
• Triangle inequality theorem( form a triangle)
• Pythagorean Theorem
• Pythagorean Inequalities
• Pythagorean Triples
In the future: rationalizing radicals & Special right triangles (2 types)
Simplify me:
1)
𝟐𝟒
𝟒
Do Now
2)
𝟑𝟔
𝟏𝟒𝟒
3)
𝟐𝟓
𝟓
*Please take notes on lined paper or in your notebooks today
Rules of Radicals
• No radicals can be in denominators…ever
We get rid of radicals in the denominators by “rationalizing” using a
“magical 1”
1
Examples on board