1. Right Triangles

2. Right Triangles A triangle with a right angle in it
Scalene Right Triangle- One right angle, two other unequal angles, no equal sides
Isosceles Right Triangle- One right angle, two other equal angles, two equal sides

3. Pythagorean Theorem
In a right angled triangle: the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Hypotenuse- the longest side of the right triangle and is always opposite of the right angle
Leg(s)- the sides of the right triangle that are on either side of the right angle

4. Pythagorean Theorem a2 + b2 = c2 A is a leg B is a leg
C is the hypotenuse

5. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle
a2 + b2 = c2
=c2
= c2
169= c2
√169 = √c2
13 =c

6. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle
a2 + b2 = c2
122 + b2=242
144 + b2 = 576
b2= 432
√b2 = √432
b =√432

7. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle
a2 + b2 = c2
72 + b2=92
49 + b2 = 81
b2= 32
√b2 = √32
b =√32

8. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle

9. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle

10. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle

11. Practice
Work on the following worksheet!

12. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle
Maria walked 3 km west and 4 km south. Calculate how far she is from her starting point.
3 km
a2 + b2 = c2
= c2
= c2
25 = c2
√ 25 = √ c2
5 = c
4 km
? km

13. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle
Lena’s guest house is 15 m long and 12 m wide. How long is the diagonal of the house?
12 km
a2 + b2 = c2
= c2
= c2
369 = c2
√ 369 = √ c2
√ 369 = c
15 km
? km

14. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle
David must install fencing around a lot that is shaped like a right triangle. The side of the lot that runs east-west is 200 ft long. The side of the lot that runs north-south is 125 ft long. Calculate how many feet of fencing he will need to surround the entire lot.
200 ft
a2 + b2 = c2
= c2
15, ,000= c2
55,625 = c2
√ 55, 625= √ c2
√ 55, 625= c
125 ft
? ft

15. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle
David must install fencing around a lot that is shaped like a right triangle. The side of the lot that runs east-west is 200 ft long. The side of the lot that runs north-south is 125 ft long. Calculate how many feet of fencing he will need to surround the entire lot.
200 ft
a2 + b2 = c2
= c2
15, ,000= c2
55,625 = c2
√ 55, 625= √ c2
√ 55, 625= c
125 ft
? ft

16. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle
A builder needs to add diagonal braces to a wall. The wall is 16 feet wide
by 12 feet high. What is the length of each brace?

17. Pythagorean Theorem a2 + b2 = c2
We use the Pythagorean Theorem to find a missing side of a right triangle
The diagram at the right shows how a post was broken. What was the original height of the post?