In your math notebook estimate each square root: 25 36 27 111 45.

In your math notebook estimate each square root: 25 36 27 111 45

Pythagorean Theorem

Pythagorean TheoremIn a right triangle, the side opposite the right

angle is the hypotenuse.

Pythagorean TheoremIn a right triangle, the side opposite the right

angle is the hypotenuse.

Pythagorean TheoremIn a right triangle, the side opposite the right

angle is the hypotenuse.

Hypotenuse

Pythagorean TheoremIn a right triangle, the side opposite the right

angle is the hypotenuse.

The hypotenuse is always the longest side.

Hypotenuse

Pythagorean TheoremLegs:

Hypotenuse

Leg

Pythagorean TheoremLegs:

Each of the sides forming the right angle.

Hypotenuse

Leg

Pythagorean TheoremThe Pythagorean Theorem describes the

relationship of the lengths of the sides of a right triangle.

Pythagorean TheoremThe Pythagorean Theorem describes the

relationship of the lengths of the sides of a right triangle.The sum of the squares of the lengths of the

legs is equal to the square of the length of the hypotenuse.

Pythagorean TheoremThe Pythagorean Theorem describes the

relationship of the lengths of the sides of a right triangle.The sum of the squares of the lengths of the

legs is equal to the square of the length of the hypotenuse.

A + B = C

Pythagorean TheoremThe Pythagorean Theorem describes the

relationship of the lengths of the sides of a right triangle.The sum of the squares of the lengths of the

legs is equal to the square of the length of the hypotenuse.

A + B = C

A

B

C

Solve to find the hypotenuse:

Solve to find the hypotenuse:

Solve to find the hypotenuse:

Using the equation:

Using the equation:We can also use the equation to find one of

the legs.

Using the equation:We can also use the equation to find one of

the legs.To find a leg, just put in what you know and

solve for the missing variable.

Solve to find the missing leg:

Solve to find the missing leg:

Solve to find the missing leg:

Pythagorean Triples:A set of three positive integers that satisfy

the set:a + b = c

Find the distance traveled:Obama is 6.1 feet tall. The pitching mound is 60.5 feet from home plate.If Obama hits the plate, how far did the ball travel?

Find the distance traveled:Cruz hits a homerun clearing the wall in center field, which is 400 feet from home plate.The wall in center field is 8 feet tall. How far did the ball travel (assume he hit it off the ground)?

Conditional:

Conditional:An if-then statement like, “If you live in El

Paso, then you are a Texan.”

Conditional:An if-then statement like, “If you live in El

Paso, then you are a Texan.”Hypothesis:

Conditional:An if-then statement like, “If you live in El

Paso, then you are a Texan.”Hypothesis:

The first part (after “if”).

Conditional:An if-then statement like, “If you live in El

Paso, then you are a Texan.”Hypothesis:

The first part (after “if”).Conclusion:

Conditional:An if-then statement like, “If you live in El

Paso, then you are a Texan.”Hypothesis:

The first part (after “if”).Conclusion:

The second part (after “then”).

Conditional:An if-then statement like, “If you live in El

Paso, then you are a Texan.”Hypothesis:

The first part (after “if”).Conclusion:

The second part (after “then”).Converse:

Conditional:An if-then statement like, “If you live in El

Paso, then you are a Texan.”Hypothesis:

The first part (after “if”).Conclusion:

The second part (after “then”).Converse:

Switches the hypothesis and conclusion.

Converse of the Pythagorean Theorem:

Converse of the Pythagorean Theorem:If a triangle has sides of lengths a, b, and c,

and a + b = c, then the triangle is a right triangle

with hypotenuse of length c.

Find if the triangle is a right triangle using the converse of the Pythagorean Theorem:

3

4

5

Find if the triangle is a right triangle using the converse of the Pythagorean Theorem:

5

6

7

Special Right Triangles:

Special Right Triangles:45 -45 -90 Triangles

Special Right Triangles:45 -45 -90 Triangles

The length of the hypotenuse = leg

Special Right Triangles:30 -60 -90 Triangles

Special Right Triangles:30 -60 -90 Triangles

Hypotenuse = short leg 2Longer leg = short leg

Find the missing sides:

45

45

3

Find the missing sides:

45

45

10

Find the missing sides:

60

30

10

Find the missing sides:

60

30

14

AssignmentPage 436-438Numbers 4-30 Even