1. Guided Notes/Practice
1/18: We will learn to apply Pythagorean Theorem to solve for missing side lengths of right triangles.
Do Now:
Have Out:
- Today’s Handouts
- HW due today
Be a Tri-Angel today
Agenda:
Do Now!
Guided Notes/Practice IP ET
Homework
Handout
(11 problems)
1st Period

2. We will learn to apply Pythagorean Theorem to solve for missing side lengths of right triangles.
Write down objective & begin Do Now!

3. it has a box (right angle)
The values in the chart represent the sides of a right triangle. Complete the chart below.
Compare the values of a2 + b2 and c2. Write an algebraic equation to represent this relationship.
Describe what the variables in your equation above represent by completing the following phrases: - ∆XYZ is a _____________ triangle because ___________________________________________________________
- a and b represent the _____________ of ∆XYZ because ________________________________________________
- c represents the __________________ of ∆XYZ because ________________________________________________ 9 16 25 25 25
144
169
169
it is opposite the right angle of the triangle
.36
.64 1 1
c2 = a2 + b2
right
it has a box (right angle)
LEGS
they form the right angle of the triangle
HYPOTENUSE

4. Pythagorean Theorem: If a triangle is a _____________ triangle,
then the square of the longest side (______________) is equal to the
____________of the squares of the other two sides (__________).
RIGHT
HYPOTENUSE
SUM
LEGS OR

5. Example 1a Pythagorean Theorem Substitute. Square.
Find the value of x. Write your answer in simplest radical form and as a decimal rounded to nearest hundredth.
SOLUTION
(hypotenuse)2
= (leg)2 + (leg)2
Pythagorean Theorem
52 = 32 + x2
Substitute.
25= 9 + x2
Square.
16 = x2
Subtract 9 from both sides
4 = x
Find the positive square root.

6. Example 1a Not possible because not a right triangle
Find the value of x. Write your answer in simplest radical form and as a decimal rounded to nearest hundredth.
SOLUTION
Not possible because not a right triangle

7. Example 1c Pythagorean Theorem Substitute. Square. Add.
Find the value of x. Write your answer in simplest radical form and as a decimal rounded to nearest hundredth. 2
SOLUTION
(hypotenuse)2
= (leg)2 + (leg)2
Pythagorean
Theorem
Substitute.
x2 =
Square.
x2 = 16
Add.
x = 4
Find the positive square root.

8. Example 1c
Maritza and Melanie run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest hundredth of a mile, they must travel to return to their starting point?

9. EXAMPLE 4
SOLUTION = +
162 = 42 + x2

10. EXAMPLE 3 Substitute. Square. Subtract 16 from each side.
Standardized Test Practice
SOLUTION
162 = 42 + x2
Substitute.
256 = 16 + x2
Square.
240 = x2
Subtract 16 from each side.
240 = x
Find positive square root.
≈ x
Approximate with a calculator.
ANSWER
The ladder is resting against the house at about 15.5 feet above the ground.
The correct answer is D.

11. Example 4 Pythagorean Theorem Substitute. Square Add.
SOLUTION
(hypotenuse)2
? (leg)2 + (leg)2
Pythagorean
Theorem
Substitute.
64 ?
Square
64 ?64
Add.
64 = 64
YES, these side lengths make a right triangle!

12. Pythagorean Triples: Any set of _____ ____________ numbers {a, b, c} that satisfies _______________.
IF it satisfies the rule stated above, then the three numbers create a _______ ____________.
three whole
c2 = a2 + b2
right
triangle
Example 5: Determine if the following sets of numbers are Pythagorean Triples. Justify your response.

13. Example 5: Determine if the following sets of numbers are Pythagorean Triples. Justify your response.
b. {7, 9, 8} c. {37, 12, 35}
c2 ? a2 + b2
c2 ? a2 + b2
372 ?
92 ?
81 ?
1369 ?
1369 = 1369
81 < 113
Since c2 < a2 + b2 then this set of numbers is NOT a Pythagorean Triple
Since c2 = a2 + b2 then this set of numbers is a Pythagorean Triple