1. Proving Right Triangles
Pythagorean Theorem
Proving Right Triangles

2. The Pythagorean Theorem
Converse of the Pythagorean Theorem The Pythagorean theorem can be written in “if-then” form.
Theorem: If a triangle is a right triangle, then a 2 + b 2 = c 2.
If you reverse the two parts of the statement, the new statement is called the converse of the Pythagorean theorem.
Converse: If a 2 + b 2 = c 2, then the triangle is a right triangle.
Although not all converses of true statements are true, the converse of the Pythagorean theorem is true. You can use it to determine whether a triangle is a right triangle.

3. The Pythagorean Theorem
EXAMPLE 3
Identifying Right Triangles
Determine whether the triangle with the given side lengths is a right triangle.
a = 3, b = 5, c = 7
SOLUTION
a 2 + b 2 = c 2
= 7 2 ?
= 49 ?
34 ≠ 49
ANSWER
Not a right triangle.

4. The Pythagorean Theorem
EXAMPLE 3
Identifying Right Triangles
Determine whether the triangle with the given side lengths is a right triangle.
a = 3, b = 5, c = 7
a = 15, b = 8, c = 17
SOLUTION
SOLUTION
a 2 + b 2 = c 2
a 2 + b 2 = c 2
= 7 2 ?
= 17 2 ?
= 49 ?
= 289 ?
34 ≠ 49
289 = 289
ANSWER
Not a right triangle.
ANSWER
A right triangle.

5. Is the following a right triangle?
4 ft
6 ft
3 ft

6. Is the following a right triangle?
8 cm
6 cm
10 cm

7. Is the following a right triangle?
7 cm
10 cm
9 cm

8. Example Which number completes the Pythagorean triple? 16, ____, 34
D. 30

9. Example Which number completes the Pythagorean triple? ____, 35, 37
D. 24

10. Example Which set of dimensions is a Pythagorean triple?
A. 6 in., 8 in., 10 in.
B. 10 in., 15 in., 18 in.
C. 15 in., 25 in., 30 in.
D. 18 in., 24 in., 27 in.

11. Example
Jacob constructed a right triangle using drinking straws. Which are possible straw lengths that formed the triangle?
A. 3 cm, 4 cm, 6 cm
B. 2 cm, 5 cm, 7 cm
C. 6 cm, 8 cm, 12 cm
D. 5 cm, 12 cm, 13 cm

12. Example Which are not the dimensions of a right triangle?
A. 3 in, 4 in, 5 in
B. 12 in, 16 in, 20 in
C. 7 in, 10 in, 16 in
D. 6 in, 8 in, 10 in

13. 5. The measures of three sides of a triangle are given below
5. The measures of three sides of a triangle are given below. Determine whether each triangle is a right triangle , 3, and 8
Which side is the biggest?
The square root of 73 (= 8.5)! This must be the hypotenuse (c).
Plug your information into the Pythagorean Theorem. It doesn’t matter which number is a or b.

14. Sides: , 3, and = ( ) 2
= 73
73 = 73
Since this is true, the triangle is a right triangle!! If it was not true, it would not be a right triangle.

15. Determine whether the triangle is a right triangle given the sides 6, 9, and
Yes No
Purple