Apply angle relationships for parallel lines cut by a transversal, including corresponding and alternate angles, vertical angles, linear pairs, and same-side interior angles, to find unknown measures, solve simple equations, and justify parallelism; determine polygon interior and exterior angles using $(n-2)180^\circ$, supplementary adjacent angles, and a $360^\circ$ exterior-angle sum for convex polygons. Identify congruent triangles using rigid motions and SSS, SAS, ASA, or AAS while rejecting SSA as sufficient, and identify similar triangles and figures using corresponding angles, proportional sides, and AA, SAS, or SSS, including rotated and reflected configurations. Use matching correspondence, scale factors, proportions, and consistent units to determine missing lengths in similar figures and triangles, solve straightforward indirect-measurement problems, and distinguish linear scale factors from additive changes.