4. BIG Ideas
The lengths of the sides of a right triangle have a special
relationship.
5. BIG Ideas
The lengths of the sides of a right triangle have a special
relationship.
If the lengths of any two sides of a right triangle are known, the
length of the third side can be found.
6. BIG Ideas
The lengths of the sides of a right triangle have a special
relationship.
If the lengths of any two sides of a right triangle are known, the
length of the third side can be found.
If the length of each side of a triangle is known, then whether the
triangle is a right triangle can be determined.
10. Vocabulary to Know
Pythagorean Theorem
In any right triangle, the sum of the squares of the lengths of the legs is
equal to the square of the length of the hypotenuse.
a2 + b2 = c2
11. Finding the Hypotenuse and Leg
Lengths
You can use the Pythagorean Theorem to find the length of a right
triangle’s hypotenuse given the lengths of its legs.
Using the Pythagorean Theorem to solve for a side length involves
finding a principal square root because side lengths are always
positive.
12. Finding the Hypotenuse
The tiles are squares with 6-in. sides. What is the length of the
hypotenuse of the right triangle shown?
6 in.
6 in.
13. Finding the Hypotenuse
The tiles are squares with 6-in. sides. What is the length of the
hypotenuse of the right triangle shown?
Use the Pythagorean Theorem
a2 + b2 = c2
6 in.
6 in.
14. Finding the Hypotenuse
The tiles are squares with 6-in. sides. What is the length of the
hypotenuse of the right triangle shown?
Use the Pythagorean Theorem
a2 + b2 = c2
Substitute 6 for a and b.
6 in.
62 + 62 = c2
6 in.
15. Finding the Hypotenuse
The tiles are squares with 6-in. sides. What is the length of the
hypotenuse of the right triangle shown?
Use the Pythagorean Theorem
a2 + b2 = c2
Substitute 6 for a and b.
6 in.
62 + 62 = c2
Simplify
36 + 36 = c2
6 in.
16. Finding the Hypotenuse
The tiles are squares with 6-in. sides. What is the length of the
hypotenuse of the right triangle shown?
Use the Pythagorean Theorem
a2 + b2 = c2
Substitute 6 for a and b.
6 in.
62 + 62 = c2
Simplify
36 + 36 = c2
6 in.
Simplify
72 = c2
17. Finding the Hypotenuse
The tiles are squares with 6-in. sides. What is the length of the
hypotenuse of the right triangle shown?
Use the Pythagorean Theorem
a2 + b2 = c2
Substitute 6 for a and b.
62 + 62 = c2
Simplify
6 in.
36 + 36 = c2
Simplify
72 = c2
6 in.
Find the principal square root.
=c
18. Finding the Hypotenuse
The tiles are squares with 6-in. sides. What is the length of the
hypotenuse of the right triangle shown?
Use the Pythagorean Theorem
a2 + b2 = c2
Substitute 6 for a and b.
62 + 62 = c2
Simplify
36 + 36 = c2
6 in.
Simplify
72 = c2
Find the principal square root.
=c 6 in.
Use a calculator
8.5 ≈ c
Convert to a fraction!!
19. Finding the Hypotenuse
The tiles are squares with 6-in. sides. What is the length of the hypotenuse of the
right triangle shown?
Use the Pythagorean Theorem
a2 + b2 = c2
Substitute 6 for a and b.
62 + 62 = c2
Simplify
36 + 36 = c2
Simplify
6 in.
72 = c2
Find the principal square root.
=c
Use a calculator 6 in.
8.5 ≈ c
Convert to a fraction!!
Write answer sentence.
The hypotenuse is 8 ½ in.
20. Finding the hypotenuse – Dry erase
practice
What is the length of the hypotenuse of a right triangle with leg
lengths 9 cm and 12 cm?
21. Finding the Length of a Leg
What is the side length b in the triangle?
5 cm 13 cm
b
22. Finding the Length of a Leg
What is the side length b in the triangle?
Use the Pythagorean Theorem.
a2 + b2 = c2
5 cm 13 cm
b
23. Finding the Length of a Leg
What is the side length b in the triangle?
Use the Pythagorean Theorem.
a2 + b2 = c2
Substitute 5 for a and 13 for c.
52 + b2 = 132
5 cm 13 cm
b
24. Finding the Length of a Leg
What is the side length b in the triangle?
Use the Pythagorean Theorem.
a2 + b2 = c2
Substitute 5 for a and 13 for c.
52 + b2 = 132
Simplify. 5 cm 13 cm
25 + b2 = 169
b
25. Finding the Length of a Leg
What is the side length b in the triangle?
Use the Pythagorean Theorem.
a2 + b2 = c2
Substitute 5 for a and 13 for c.
52 + b2 = 132
Simplify. 5 cm 13 cm
25 + b2 = 169
Remember how we solve equations. We need to isolate the
variable by using the inverse operation.
b
26. Finding the Length of a Leg
What is the side length b in the triangle?
Use the Pythagorean Theorem.
a2 + b2 = c2
Substitute 5 for a and 13 for c.
52 + b2 = 132
Simplify. 5 cm 13 cm
25 + b2 = 169
Remember how we solve equations. We need to isolate the
variable by using the inverse operation.
Subtract 25 from each side.
b2 = 144
b
27. Finding the Length of a Leg
What is the side length b in the triangle?
Use the Pythagorean Theorem.
a2 + b2 = c2
Substitute 5 for a and 13 for c.
52 + b2 = 132
Simplify. 5 cm 13 cm
25 + b2 = 169
Remember how we solve equations. We need to isolate the
variable by using the inverse operation.
Subtract 25 from each side.
b2 = 144
b
Find the principal square root of each side.
b = 72
28. Find the Length of a Leg – Dry Erase
Practice
What is the side length a in the triangle?
12
a 15
29. Vocabulary to Know
Conditional
An if-then statement such as “If an animal is a horse, then it has four
legs.”
30. Vocabulary to Know
Hypothesis
The “if” part of the conditional.
Conclusion
The “then” part of the conditional.
Converse
Switches the hypothesis and conclusion.
31. Conditional
You can write the Pythagorean Theorem as a conditional:
“If a triangle is a right triangle with legs of lengths a and b and
hypotenuse of length c, then a2 + b2 = c2.
The converse of the Pythagorean Theorem is always true.
32. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
6 in., 24 in., 25 in.
4 m, 8 m, 10 m
10 in., 24 in., 26 in.
8 ft., 15 ft., 16 ft.
33. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
6 in., 24 in., 25 in.
62 + 242 ___ 252
34. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
6 in., 24 in., 25 in.
62 + 242 ___ 252
36 + 576 ___ 625
35. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
6 in., 24 in., 25 in.
62 + 242 ___ 252
36 + 576 ___ 625
612 ≠ 625
NO
36. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
4 m, 8 m, 10 m
42 + 82 = 102
37. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
4 m, 8 m, 10 m
42 + 82 ___ 102
16 + 64 ___ 100
38. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
4 m, 8 m, 10 m
42 + 82 ___ 102
16 + 64 ___ 100
80 ≠ 100
NO
39. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
10 in., 24 in., 26 in.
102 + 242 ___ 262
100 + 576 ___ 676
40. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
10 in., 24 in., 26 in.
102 + 242 ___ 262
100 + 576 ___ 676
676 = 676
YES
41. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
8 ft., 15 ft., 16 ft.
82 + 152 ___ 162
42. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
8 ft., 15 ft., 16 ft.
82 + 152 ___ 162
64 + 225 ___ 256
43. Identifying Right Triangles
Which set of lengths could be the side lengths of a right triangle?
8 ft., 15 ft., 16 ft.
82 + 152 ___ 162
64 + 225 ___ 256
289 ≠ 256
44. Identifying Right Triangles
Dry Erase Practice
Could the lengths 20 mm, 47 mm, and 52 mm be the side lengths of
a right triangle? Explain.
46. BIG Ideas
The lengths of the sides of a right triangle have a special
relationship.
If the lengths of any two sides of a right triangle are known, the
length of the third side can be found.
If the length of each side of a triangle is known, then whether the
triangle is a right triangle can be determined.
This assignment is for Algebra I Foundation by Pearson. It was the recommended assignment for a block schedule. I usually end up altering assignments since I teach Special Education.
