1. 4.5 The Converse of the Pythagorean Theorem
Objective: Use the Converse of Pythagorean Theorem. Use side lengths to classify triangles.

2. Warm up: 1. What is the Pythagorean Theorem?
𝑎 2 + 𝑏 2 = 𝑐 2 where “c” is the longest side (hypotenuse)
2. When do we use the Pythagorean Theorem?
Use in RIGHT triangles to find the side lengths

3. 𝐼𝑓 𝑎 2 + 𝑏 2 = 𝑐 2 , 𝑡ℎ𝑒𝑛 ∆𝐴𝐵𝐶 𝑖𝑠 𝑎 𝒓𝒊𝒈𝒉𝒕 𝑡𝑟𝑖𝑎𝑛𝑔𝑙𝑒.

4. a= 12 b= 16 c= 20 longest side
𝑎 2 + 𝑏 2 ? 𝑐 2
(12) 2 + (16) 2 ? (20) 2
? 400
400 ? 400
𝑎 2 + 𝑏 2 𝑑𝑜𝑒𝑠 𝑒𝑞𝑢𝑎𝑙 𝑐 2 , 𝑡ℎ𝑒𝑛
∆𝐴𝐵𝐶 𝑖𝑠 𝑎 𝑅𝐼𝐺𝐻𝑇 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒
400 = 400

5. Classifying Triangles: In ∆𝐴𝐵𝐶 with longest side c
You can determine whether a triangle is acute, right, or obtuse by its side lengths.

6. a= 4 b= 5 c= longest side
𝑎 2 + 𝑏 2 ? 𝑐 2
(4) 2 + (5) 2 ? ( 35 ) 2
? 35
41 ? 35
𝑐 2 𝑖𝑠 𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 𝑎 2 + 𝑏 2 , 𝑡ℎ𝑒𝑛
∆𝐴𝐵𝐶 𝑖𝑠 𝑎𝑛 𝐴𝐶𝑈𝑇𝐸 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒
41 > 35

7. a= 8 b= 12 c= 15 longest side
𝑎 2 + 𝑏 2 ? 𝑐 2
(8) 2 + (12) 2 ? (15) 2
? 225
208 ? 225
𝑐 2 𝑖𝑠 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 𝑎 2 + 𝑏 2 , 𝑡ℎ𝑒𝑛
∆𝐴𝐵𝐶 𝑖𝑠 𝑎𝑛 𝑂𝐵𝑇𝑈𝑆𝐸 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒
208 < 225

8. a= 5 b= 6 c= 8 longest side
𝑎 2 + 𝑏 2 ? 𝑐 2
(5) 2 + (6) 2 ? (8) 2
? 64
61 ? 64
𝑐 2 𝑖𝑠 𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 𝑎 2 + 𝑏 2 , 𝑡ℎ𝑒𝑛
∆𝐴𝐵𝐶 𝑖𝑠 𝑎𝑛 𝑂𝐵𝑇𝑈𝑆𝐸 𝑇𝑟𝑖𝑎𝑛𝑔𝑙𝑒
61 < 64

9. 52 > 49
1369=1369
The triangle is acute.
The triangle is right.

10. You Try!
29 < 36
289=289
98 >49
Obtuse
Right
Acute

11. 625 >576
625=625
625 <676
Acute
Right
Obtuse

12. 32 >25
180 <196
225=225
Acute
Obtuse
Right