1. Pythagorean
Theorem
Solving Right Triangles

2. Solving Right Triangles
Directions
As you view this presentation, take
notes and work out the practice
problems.
When you get to the practice problem
screens, complete the step in your
notebook before continuing to the
next slide.

3. The Right Triangle
• A right triangle has one 90o
angle, A 90o angle is also called
a right angle. You know which
angle is the right angle because
it will have a box at the angle.
• The side across from the right angle
is called the hypotenuse and is
usually labeled with the letter c,
• The other two sides are called legs
and are usually labeled with the
letters a and b.
c
a
b

4. PythagoreanTheorem
• The mathematician Pythagoras proved the relationship
between the sides of a right triangle and the hypotenuse.
This relationship is known as the Pythagorean Theorem
c
b
a

5. Finding the Hypotenuse of a
Right Triangle
Practice Problem 1
Step 1: Substitute the
values of a and b
into a2 +b2 = c2.
c = ?
b = 5
a = 12

6. Finding the Hypotenuse of a
Right Triangle
Practice Problem 1
Step 1: Substitute the
values of a and b
into a2 +b2 = c2.
c = ?
b = 5
a = 12122 +52 = c2

7. Finding the Hypotenuse of a
Right Triangle
Practice Problem 1
Step 1: 122 + 52 = c2
c = ?
b = 5
a = 12
Step 2: Do the math.

8. Finding the Hypotenuse of a
Right Triangle
Practice Problem 1
Step 1: 122 + 52 = c2
c = 13
b = 5
a = 12
Step 2: Do the math.

9. Finding the Hypotenuse of a
Right Triangle
Practice Problem 2
Step 1: Substitute the
values of a and b
into a2 +b2 = c2.
c = ?
b = 5
a = 6

10. Finding the Hypotenuse of a
Right Triangle
Practice Problem 2
Step 1: Substitute the
values of a and b
into a2 +b2 = c2.
c = ?
b = 5
a = 662 + 52 = c2

11. Finding the Hypotenuse of a
Right Triangle
Practice Problem 2
Step 1: 62 + 52 = c2
c = ?
b = 5
a = 6
Step 2: Do the math.

12. Finding the Hypotenuse of a
Right Triangle
Practice Problem 2
Step 1: 62 + 52 = c2
b = 5
a = 6
Step 2: Do the math.
Note: c2 is not always a
perfect square. Always read
directions carefully to know
what form your answer
should take.

13. Finding a Leg of a Right Triangle
Practice Problem 1
Step 1: Substitute the values
of a and c into a2 +b2 = c2.
c = 10
b = 8
a = ?

14. Finding a Leg of a Right Triangle
Practice Problem 1
Step 1: Substitute the values
of a and c into a2 +b2 = c2.
c = 10
b = 8
a = ?
a2 + 82 = 102

15. Finding a Leg of a Right Triangle
Practice Problem 1
Step 1: Substitute the values
of a and c into a2 +b2 = c2.
c = 10
b = 8
a = ?
a2 + 82 = 102
Step 2: Do the math.

16. Finding a Leg of a Right Triangle
Practice Problem 1
Step 1: Substitute the values
of a and c into a2 +b2 = c2.
c = 10
b = 8
a = 6
a2 + 82 = 102
Step 2: Do the math.
a2 + 64 = 100
a2 = 36
a = 6

17. Finding a Leg of a Right Triangle
Practice Problem 2
Step 1: Substitute the values
of b and c into a2 + b2 = c2.
c = 9
b = ?
a = 5

18. Finding a Leg of a Right Triangle
Practice Problem 2
Step 1: Substitute the values
of b and c into a2 + b2 = c2.
c = 9 b = ?
a = 5
52 + b2 = 92

19. Finding a Leg of a Right Triangle
Practice Problem 2
Step 1: 52 + b2 = 92.
c = 9 b = ?
a = 5
Step 2: Do the math.

20. Finding a Leg of a Right Triangle
Practice Problem 2
Step 1: 52 + b2 = 92.
c = 9
a = 5
Step 2: Do the math.
Note: You should always
simplify the square root if
possible.