Classify triangles by angle measures and side-length relationships, use the $180^\circ$ triangle angle sum to determine unknown angles, and construct triangles from given side or angle measurements using the triangle inequality and angle-sum constraints. Identify complementary and supplementary angles, and determine unknown angles formed by intersecting lines using vertical-angle equality and linear-pair sums of $180^\circ$, including simple numerical or algebraic equations. Classify quadrilaterals by properties such as parallel or perpendicular sides, equal side lengths, and angle relationships, recognizing inclusive categories among parallelograms, rectangles, rhombi, squares, kites, and trapezoids.