Chapter 5

Example 1

Example 2

Example 3

Example 4

Example 5

Pg 304: 2-4, 12-17

Homework

Name: Entrance TicketUse 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 b. Construct the perpendicular bisectors of . 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 Now1) 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

Triangle Inequality Theorem Verify: orange +yellow > pink pink + yellow > orange

AB + BC > AC

BC+ AC > AB

AC + AB > BC

The sum of the lengths of ANY

sides of a triangle must be greater

than the length of the third side.

10cm7cm

9cm

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 side14, 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

Do Now • Simplify:

• In a right triangle a=6 and c =10 solve for b

• Simplify

• Simplify

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

24

x

What about acute & obtuse triangles?

Is there a relationship??

c b

a

c

ba

8

9

10

.5 .55

.25

4 5

6

6 5

10

3

7

9 45/47/2

15/2

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)

Do Now Simplify me:

1) 2) 3)

*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