1. 7.1 Apply the Pythagorean Theorem
7.1
Video attached
Bell Thinger
1. Solve x2 = 100.
ANSWER
10, –10
4. Find x.
2. Solve x2 + 9 = 25.
ANSWER
4, –4
3. Simplify 20.
ANSWER
2 5
ANSWER
6 cm

2. 7.1

3. Example 1
7.1
Find the length of the
hypotenuse of the right
triangle.
SOLUTION
(hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem
x 2 = 62 + 82
Substitute.
x2 = 36 + 64
Multiply.
x2 = 100
Add.
x = 10
Find the positive square root.

4. Guided Practice
7.1
Identify the unknown side as a leg or hypotenuse.
Then, find the unknown side length of the right
triangle. Write your answer in simplest radical form.
1.
ANSWER
Leg; 4

5. Guided Practice
7.1
Identify the unknown side as a leg or hypotenuse.
Then, find the unknown side length of the right
triangle. Write your answer in simplest radical form.
2.
ANSWER
hypotenuse; 2 13

6. Example 2
7.1
SOLUTION
=
+

7. Example 2
7.1
162 = 42 + x2
Substitute.
256 = 16 + x2
Multiply.
240 = x2
Subtract 16 from each side.
√240 = x
Find positive square root.
15.492 ≈ x
Approximate with a calculator.
The ladder is resting against the house at about 15.5
feet above the ground.
ANSWER
The correct answer is D.

8. Guided Practice
7.1
3. The top of a ladder rests against a wall, 23 feet
above the ground. The base of the ladder is 6 feet
away from the wall. What is the length of the
ladder?
ANSWER
about 23.8 ft

9. Guided Practice
7.1
4. The Pythagorean Theorem is only true for what type
of triangle?
ANSWER right triangle

10. Example 3
7.1
Find the area of the isosceles triangle with side
lengths 10 meters, 13 meters, and 13 meters.
SOLUTION
STEP 1 Draw a sketch. By definition,
the length of an altitude is the height
of a triangle. In an isosceles triangle,
the altitude to the base is also a
perpendicular bisector. So, the
altitude divides the triangle into two
right triangles with the dimensions
shown.

11. Example 3
7.1
STEP 2 Use the Pythagorean Theorem to find the
height of the triangle.
c2 = a2 + b2
Pythagorean Theorem
Substitute.
132 = 52 + h2
Multiply.
169 = 25 + h2
Subtract 25 from each side.
144 = h2
12 = h
Find the positive square root.
STEP 3 Find the area.
1
Area = 1 (base) (height) = (10) (12) = 60 m2
2
2
The area of the triangle is 60 square meters.

12. Guided Practice
7.1
Find the area of the triangle.
5.
ANSWER about 149.2 ft2

13. Guided Practice
7.1
Find the area of the triangle.
6.
ANSWER 240 m2.

14. 7.1

15. Example 4
7.1
Find the length of the hypotenuse
of the right triangle.
SOLUTION
Method 1: Use a Pythagorean triple.
A common Pythagorean triple is 5, 12, 13. Notice that if
you multiply the lengths of the legs of the Pythagorean
triple by 2, you get the lengths of the legs of this
triangle: 5 . 2 = 10 and 12. 2 = 24. So, the length of the
hypotenuse is 13 . 2 = 26.

16. Example 4
7.1
Method 2: Use the Pythagorean Theorem.
x2 = 102 + 242
Pythagorean Theorem
x2 = 100 + 576
Multiply.
x2 = 676
Add.
x = 26
Find the positive square root.

17. Guided Practice
7.1
Find the unknown side length of the right triangle
using the Pythagorean Theorem. Then use a
Pythagorean triple.
7.
ANSWER
15 in.

18. Guided Practice
7.1
Find the unknown side length of the right triangle
using the Pythagorean Theorem. Then use a
Pythagorean triple.
8.
ANSWER
50 cm.

19. Exit Slip
7.1
1.
Find the length of the hypotenuse of the right
triangle.
ANSWER
39

20. Exit Slip
7.1
2.
Find the area of the isosceles triangle.
ANSWER
1080 cm2

21. Exit Slip
7.1
3.
Find the unknown side length x. Write your answer
in simplest radical form.
ANSWER
4 13

22. Exit Slip
7.1
Extra practice

23. 7.1

24. 7.1
Homework
Pg 454-457
#5, 12, 16, 26, 31