clickers. yesterday we reviewed the pythagorean theorem today we’re going to extend the theorem...

BellworkWill the following side lengths make a triangle?•1, 3, 10•3.2, 11, 6.9•3, 4, 5

Clickers

Bellwork SolutionWill the following side lengths make a triangle?•1, 3, 10

.

.

A Yes

B No

Bellwork SolutionWill the following side lengths make a triangle?•3.2, 11, 6.9

.

.

A Yes

B No

Bellwork SolutionWill the following side lengths make a triangle?•3, 4, 5

.

.

A Yes

B No

Using the Converse of the Pythagorean Theorem

Section 7.2

The Concept Yesterday we reviewed the Pythagorean Theorem Today we’re going to extend the Theorem to discuss

how it works within any triangle This is a precursor to the Law of Sines and Law of

Cosines that we’ll discuss post EOC.

A QuestionWhat kind of triangle will the following side lengths make ?• 11, 3, 10• 5,10, 6• 3, 4, 5

Not exactly Chuck TaylorTheorem 7.2 Converse of the Pythagorean Theorem

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle

or

If a2+b2=c2 then the triangle is right

a

b

c

ExampleIs the triangle a right triangle?

5

13

14

A. Yes

B. No

ExampleIs the triangle a right triangle?

10

12

2 61

A. Yes

B. No

Practical ExampleOne of the most common uses of this converse is in building

applicationsFor example:

You and a friend are laying out a deck that is going to 10 ft. by 15 ft.. You measure the diagonal formed and find it to be 17.5 ft. Are the boards you’ve laid out square? (i.e. do they form a right angle?

15’

10’

2 2 210 15 17.5

10’

15’

17.5’

100 225 306.25 325 306.25

Question:Do the boards need to be widened

or pulled back in?

Tying Pythagoras to acute and obtuseTheorem 7.3

If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle.orIf c2<a2+b2 then the triangle is acute

Theorem 7.4 If the square of the length of the longest side of a triangle is more than the sum of the squares of the lengths of the other two sides, then the triangle is an obtuse triangle.orIf c2>a2+b2 then the triangle is obtuse

On your ownIs this triangle acute, right or obtuse?

Legs: 7.5, 8Hypotenuse: 11.1

A. Acute

B. Right

C. Obtuse

On your ownIs this triangle acute, right or obtuse?

Legs: 6, 9Hypotenuse: 10

A. Acute

B. Right

C. Obtuse

On your ownIs this triangle acute, right or obtuse?

Legs: 5, 12Hypotenuse: 13

A. Acute

B. Right

C. Obtuse

Practical example

You walk 749 feet due east to the gym from your home. From the gym you walk 800 feet southwest to the library. Finally, you walk 305 feet from the library back home. Do you live directly north of the library?

A. Yes

B. No

C. IDK

Homework

7.215-23, 29, 30, 33

Most Important Points• Pythagorean Theorem• When to use radicals and when to use decimals