6. Inequalities in Two Triangles
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Identify congruent sides in the triangles.
SR>XY
Let's copy the diagram and highlight the segments we are asked to compare.
We can see that two sides of △ RTS are congruent to two sides of △ YZX. However, the included angle in △ RTS is larger than the included angle in △ YZX. RT≅YZ TS≅ZX m∠ RTS> m∠ YZX According to the Hinge Theorem, the third side of △ RTS is longer than the third side of △ YZX. SR> XY