Geometry and Measurement
What to know
Geometry and measurement spans angle relationships, polygon properties, congruence and similarity, the Pythagorean theorem, perimeter, area, surface area, volume, circles, transformations, and coordinate geometry. Know that the interior angles of a triangle sum to 180° and of an n-gon to (n−2)180°; that similar figures have equal angles and proportional sides; and that the Pythagorean theorem applies only to right triangles. Measurement items test unit conversion, scale drawings, precision, and choosing appropriate units.
Traps
Radius versus diameter is the classic error: circumference is πd or 2πr, while area is πr². Doubling the radius quadruples area but only doubles circumference. Convert units before computing, and remember square and cubic units scale by the square and cube of the factor-1 m² = 10,000 cm². In prisms and cylinders, use perpendicular height, not slant height. Similar figures preserve shape, not size; congruent figures preserve both.
Worked example
A circle has radius 5 cm. Circumference = 2π(5) = 10π cm; area = π(5²) = 25π cm². If the radius doubles to 10 cm, area becomes 100π, four times larger. Rule of thumb: before computing, ask whether the quantity is one-dimensional (length), two-dimensional (area), or three-dimensional (volume), then attach the matching unit.