Understanding Pythagorean Triples and Patterns

The video tutorial introduces the Pythagorean theorem and explores Pythagorean triples, which are sets of whole numbers that satisfy the theorem. It identifies patterns in these triples and presents formulas to generate them. The tutorial further explains a generalized formula for creating Pythagorean triples and provides examples to illustrate its application. The video concludes with a discussion on the significance of these patterns and formulas in understanding right triangles.

Which of the following is a Pythagorean triple?

• 5, 6, 7

• 2, 3, 4

• 3, 4, 5

• 1, 2, 3

Tags

CCSS.8.G.B.8

What is the pattern observed in the Pythagorean triples like 3-4-5 and 5-12-13?

• 'c' is 'b+3'

• 'a' increases by 2

• 'c' is 'b+2'

• 'a' increases by 3

For the formula generating Pythagorean triples with odd 'a', what is 'b' when 'x' is 3?

• 4

• 5

• 6

• 7

Tags

CCSS.8.G.B.8

In the formula for even 'a' triples, what is the relationship between 'c' and 'b'?

• 'c' is 'b+3'

• 'c' is 'b+1'

• 'c' is 'b+2'

• 'c' is 'b+4'

Tags

CCSS.HSF-IF.C.8A

CCSS.HSA-SSE.B.3B

What is the formula for 'b' in the even 'a' triples?

• 1/2 x^2 + 1/2

• 1/4 x^2 + 1

• 1/4 x^2 - 1

• 1/2 x^2 - 1/2

What is the generalized formula for 'b' in triples where 'c' is 'b+8'?

• 1/8 x^2 - 4

• 1/2 x^2 - 4

• 1/16 x^2 - 4

• 1/4 x^2 - 4

Tags

CCSS.8.G.B.8

In the generalized formula, what is the value of 'z' for triples where 'c' is 'b+9'?

• 8

• 9

• 10

• 11

Tags

CCSS.HSG.SRT.C.8

For triples where 'c' is 'b+18', what is the formula for 'c'?

• 1/18 x^2 + 9

• 1/9 x^2 + 9

• 1/4 x^2 + 9

• 1/36 x^2 + 9

What is the pattern in the triples where 'c' is 'b+25'?

• 'a' increases by 10

• 'a' increases by 15

• 'a' increases by 5

• 'a' increases by 20

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

What happens to the 75-100-125 triangle when reduced?

• Becomes 3-4-5

• Becomes 5-12-13

• Becomes 6-8-10

• Becomes 7-24-25

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6