Warm UpClassify each triangle by its angle measures.

1. 2.

3. Simplify

4. If a = 6, b = 7, and c = 12, find a2 + b2 and find c2. Which value is greater?

acute right

12

85; 144; c2

Geometry drill 1/2/14

Which is the largest angle and why?

Objective SW define and apply the Pythagorean Theorem so that they can find the dimensions of geometric figures.

Right Triangle Def.Legs-__________

c

b

a

Right Triangle Def.Legs-__________

c

b

a

a and b

Right Triangle Def.Legs-__________Hypotenuse-______

a and b

c

b

a

Right Triangle Def.Legs-__________Hypotenuse-______

c

b

a

a and b

c

HypotenuseThe ________ side of a right triangle across from the ________ angle.

HypotenuseThe ________ side of a right triangle across from the ________ angle.

longest

right

Pythagorean Theorem For any right triangle, the sum of the square of the two ___

c

b

a

is equal to the square of the _________.

Pythagorean Theorem For any right triangle, the sum of the square of the two ___

c

b

a

is equal to the square of the _________.

legs

hypotenuse

Pythagorean Theorema2+b2=c2

c

b

a

Corollary to the Pythagorean Theorem

If the sum of the squares of the two shorter sides of a triangle is less than the square of the longest side, then the triangle is ______.

Corollary to the Pythagorean Theorem

If the sum of the squares of the two shorter sides of a triangle is less than the square of the longest side, then the triangle is ______.obtuse

Corollary to the Pythagorean Theorem

If the sum of the squares of the two shorter sides of a triangle is greater than the square of the longest side, then the triangle is ______.

Corollary to the Pythagorean Theorem

If the sum of the squares of the two shorter sides of a triangle is greater than the square of the longest side, then the triangle is ______.

acute

Corollary to the Pythagorean Theorem

If the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is ______.

Corollary to the Pythagorean Theorem

If the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is ______.right

Corollary to the Pythagorean Theorem

a2+b2>c2 acute a2+b2<c2 obtuse a2+b2=c2 right

Is the following triangle acute, obtuse or right?

15

10

12

Is the following triangle acute, obtuse or right?

5

4

3

Is the following triangle acute, obtuse or right?

20

10

12

ConclusionSummarize the corollary to the Pythagorean theorem:

1. Find the value of x.

2. An entertainment center is 52 in. wide and 40 in. high. Will a TV with a 60 in. diagonal fit in it? Explain.

12