Chapter 4 - Congruent Triangles - 4-2 Triangle Congruence by SSS and SAS - Practice and Problem-Solving Exercises - Page 231: 18

△ABC and △DEF are congruent using Postulate 4-1 Side-Side-Side (SSS) Postulate

Distance Formula 𝑑 = √(𝑥₂ - 𝑥₁)² + (𝑦₂ - 𝑦₁)² △ABC Distance from A(1,4) to B(5,5) 𝑑 = √(5 - 1)² + (5 - 4)² 𝑑 = √(4)² + (1)² 𝑑 = √16 + 1 𝑑 = √17 𝑑 ≈ 4.12 Distance from B(5,5) to C(2,2) 𝑑 = √(2 - 5)² + (2 - 5)² 𝑑 = √(-3)² + (-3)² 𝑑 = √9 + 9 𝑑 = √18 𝑑 ≈ 4.24 Distance from C(2,2) to A(1,4) 𝑑 = √(1 - 2)² + (4 - 2)² 𝑑 = √(-1)² + (2)² 𝑑 = √1 + 4 𝑑 = √5 𝑑 ≈ 2.24 △DEF Distance from D(-5,1) to E(-1,0) 𝑑 = √(-1 - -5)² + (0 - 1)² 𝑑 = √(4)² + (-1)² 𝑑 = √16 + 1 𝑑 = √17 𝑑 ≈ 4.12 Distance from E(-1,0) to F(-4,3) 𝑑 = √(-4 - -1)² + (3 - 0)² 𝑑 = √(-3)² + (3)² 𝑑 = √9 + 9 𝑑 = √18 𝑑 ≈ 4.24 Distance from F(-4,3) to D(-5,1) 𝑑 = √(-5 - -4)² + (1 - 3)² 𝑑 = √(-1)² + (-2)² 𝑑 = √1 + 4 𝑑 = √5 𝑑 ≈ 2.24 AB ≅ DE = √17 ≈ 4.12 BC ≅ EF = √18 ≈ 4.24 CA ≅ FD = √5 ≈ 2.24 △ABC ≅ △DEF - Postulate 4-1 Side-Side-Side (SSS) Postulate