1. Unit 6 Lesson 3 The Pythagorean Converse
CCSS
Lesson Goals
G-SRT 4: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Apply the Pythagorean Converse to classify a triangle according to angle measure.
ESLRs: Becoming Effective Communicators,
Competent Learners and Complex Thinkers

2. Draw
In the Column Q’s section of your notes, attempt to draw a triangle with 1,1,and 3 cm sides.
Then attempt to draw one with 4,4, and 3 cm sides
Then attempt to draw one with 3,3, and 5 cm sides.
Analyze and compare their differences with a student next to you.

3. Theorem Triangle Inequality Theorem
The length of the longest side of a triangle must be less than the sum of the lengths of the two shorter sides. A B C B A C B C

4. You Try
Can a triangle be constructed with sides of the following measures?
5, 7, 8
8 < 5 + 7
Yes
The length of the longest of a triangle must be less
than the sum of the lengths of the two shorter sides.

5. You Try
Can a triangle be constructed with sides of the following measures?
4.2, 4.2,
8.4 < NO
The length of the longest of a triangle must be less
than the sum of the lengths of the two shorter sides.

6. You Try
Can a triangle be constructed with sides of the following measures?
3, 6, 10
10 < 3 + 6 NO

7. You Try
Can a triangle be constructed with sides of the following measures?
3, 3, 8
8 < 3 + 3 NO

8. You try
Can a triangle be constructed with sides of the following measures?
9, 5, 11
11 < 9 + 5
Yes

9. Theorem The Pythagorean Converse Keep the longest length on the left!
A triangle can be classified according to angles measurement by comparing the square of the longest side of the triangle to the sum of the squares of the
other two sides
Keep the longest length on the left!

10. example
Classify the triangle as right, acute, or obtuse. 8 7
right

11. example obtuse Classify the triangle as right, acute, or obtuse. 13 107
obtuse

12. example
Decide whether the set of numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse.
8, 18, and 24
To be a triangle, the longest side must
be less than the sum of other two sides.

13. example
Decide whether the set of numbers can represent the side
lengths of a triangle. If they can, classify the triangle as
right, acute, or obtuse.
8, 18, and 24
Use the Pythagorean Converse to classify the triangle.
obtuse

14. You Try
Decide whether the set of numbers can represent the side lengths of a triangle.
32, 48, and 51
To be a triangle, the longest side must
be less than the sum of other two sides.

15. You Try
Classify the triangle as right, acute, or obtuse.
32, 48, and 51
Use the Pythagorean Converse to classify the triangle.
acute

16. You Try
Decide whether the set of numbers can represent the side lengths of a triangle.
8, 40, 41
obtuse

17. You Try
Decide whether the set of numbers can represent the side lengths of a triangle.
12.3, 16.4, 20.5
right

18. example
Find the range of values for c, the longest side of the triangle, so that the triangle is acute when a = 8 and b = 14. 8 c 14 A B C
16.1

19. example
Find the range of values for c, the longest side of the triangle, so that the triangle is obtuse when a = 12 and b = 15. 12 c 15 A B C
19.2

20. You Try
Find the range of values for c, the longest side of the triangle, so that the triangle is obtuse when a = 7 and b = 16. 7 c 16 A B C
17.5

21. Example B
Obtuse Triangle C A

22. Summary
Create an acronym, poem, or mnemonic to help you remember the Pythagorean Converse.

23. Today’s Assignment p. 546: 14 – 20 e; 32, 33, 34 +
Find the value for c, the longest side of the
triangle, so that the triangle is a) acute
and b) obtuse.
5, 11
12, 17

24. Find the value for c, the longest side of the triangle, so that the triangle is a) acute and b) obtuse.
+1) 5, 11
+2) 12, 17