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Expectations/Procedures Triangle Congruency (Geometry Review) Four triangle congruence theorems: We can use trigonometry to find the other parts of the triangle once congruence is established. Law of Sines Given any ABC with angles A,B,C and opposite sides a,b,c respectively. 𝑠𝑖𝑛𝐴 𝑎 = 𝑠𝑖𝑛𝐵 𝑏 = 𝑠𝑖𝑛𝐶 𝑐 • Use when you have AAS or ASA to find the other side lengths. • Use when you have SSA to find the angle opposite the other given side. Example (AAS) Solve ABC given A = 38 B = 46 and a = 9. Example – You Try (ASA) Solve ABC given A = 60 B = 45 and c = 5.1 SSA Case • Since SSA does not determine its size and shape, there might be one, two, or zero triangles determined. Example (SSA) State whether the given measurements determine zero, one, or two triangles. Then solve the triangle. A = 73 a = 24 and b = 28 Example (SSA) State whether the given measurements determine zero, one, or two triangles. Then solve the triangle. B = 82 b = 17 and c = 15 Example (SSA) State whether the given measurements determine zero, one, or two triangles. Then solve the triangle. A = 30 a = 6 and b = 7 Example • A forest ranger at station A sights a fir in the direction 32 east of north. A second forest ranger at station B, 10 miles due east of A, sights the same fire on a line 48 west of north. Find the distance from each ranger station to the fire. Homework • 5.5 (pg. 439) #4,6,14-16,37