1. Lesson 4 Menu Five-Minute Check (over Lesson 10-3) Main Ideas and Vocabulary Targeted TEKS Key Concept: The Pythagorean Theorem Example 1: Find the Length of the Hypotenuse Example 2: Find the Length of a Side Example 3: Pythagorean Triples Key Concept: Converse of the Pythagorean Key Concept: Converse of the Pythagorean TheoremTheorem Example 4: Check for Right Triangles

2. Lesson 4 MI/Vocab hypotenuse legs Pythagorean triple converse Solve problems by using the Pythagorean Theorem. Determine whether a triangle is a right triangle.

3. Key Concept 10-4a

4. Lesson 4 Ex1 Find the Length of the Hypotenuse Find the length of the hypotenuse of a right triangle if a = 18 and b = 24. c 2 = a 2 + b 2 Pythagorean Theorem c 2 = 18 2 + 24 2 a = 18 and b = 24 c 2 = 900Simplify. Answer: The length of the hypotenuse is 30 units. Take the square root of each side. Use the positive value.

5. A.A B.B C.C D.D Lesson 4 CYP1 A.45 units B.85 units C.65 units D.925 units Find the length of the hypotenuse of a right triangle if a = 25 and b = 60.

6. Lesson 4 Ex2 Find the Length of a Side Find the length of the missing side. If necessary, round to the nearest hundredth. c 2 = a 2 + b 2 Pythagorean Theorem 16 2 = 9 2 + b 2 a = 9 and c = 16 256 = 81 + b 2 Evaluate squares. 175 = b 2 Subtract 81 from each side. Answer: about 13.23 units Use the positive value.

7. Lesson 4 CYP2 1.A 2.B 3.C 4.D A.about 12 units B.about 22 units C.about 16.25 units D.about 5 units Find the length of the missing side.

8. Lesson 4 Ex3 STANDARDIZED TEST PRACTICE What is the area of triangle XYZ? A 94 units 2 B 128 units 2 C 294 units 2 D 588 units 2 Pythagorean Triples Read the Test Item

9. Lesson 4 Ex3 Solve the Test Item Step 1Check to see if the measurements of this triangle are a multiple of a common Pythagorean triple. The hypotenuse is 7 ● 5 units and the leg is 7 ● 4 units. This triangle is a multiple of a (3, 4, 5) triangle. 7 ● 3 = 21 7 ● 4 = 28 7 ● 5 = 35 The height of the triangle is 21 units. Pythagorean Triples

10. Lesson 4 Ex3 Step 2Find the area of the triangle. Answer: The area of the triangle is 294 square units. Choice C is correct. Pythagorean Triples Area of a triangle b = 28 and h = 21 Simplify.

11. 1.A 2.B 3.C 4.D Lesson 4 CYP3 A.764 units 2 B.480 units 2 C.420 units 2 D.384 units 2 STANDARDIZED TEST PRACTICE What is the area of triangle RST?

12. Key Concept 10-4b

13. Lesson 4 Ex4 A. Determine whether the side measures of 7, 12, 15 form a right triangle. Since the measure of the longest side is 15, let c = 15, a = 7, and b = 12. Then determine whether c 2 = a 2 + b 2. Answer: Since c 2 ≠ a 2 + b 2, the triangle is not a right triangle. Check for Right Triangles 225= 49 + 144Multiply. ? ? 15 2 = 7 2 + 12 2 a = 7, b = 12, and c = 15 225≠ 193Add. c 2 = a 2 + b 2 Pythagorean Theorem

14. Lesson 4 Ex4 B. Determine whether the side measures of 27, 36, 45 form a right triangle. Check for Right Triangles Since the measure of the longest side is 45, let c = 45, a = 27, and b = 36. Then determine whether c 2 = a 2 + b 2. Answer: Since c 2 = a 2 + b 2, the triangle is a right triangle. c 2 = a 2 + b 2 Pythagorean Theorem 45 2 = 27 2 + 36 2 a = 27, b = 36, and c = 45 2025 = 729 + 1296Multiply. 2025 = 2025Add.

15. 1.A 2.B 3.C Lesson 4 CYP4 A.right triangle B.not a right triangle C.cannot be determined A. Determine whether the following side measures form right triangles: 33, 44, 55.

16. 1.A 2.B 3.C Lesson 4 CYP4 A.right triangle B.not a right triangle C.cannot be determined B. Determine whether the following side measures form right triangles: 15, 12, 24.