Geometry and Measurement
What this domain tests
Geometry and Measurement tests angle relationships, properties of triangles and quadrilaterals, similarity and congruence, the Pythagorean theorem, perimeter, area, surface area, volume, coordinate geometry, and unit conversion.
Core rules
- Angles on a line sum to 180°; angles around a point sum to 360°; vertical angles are equal. The interior angle sum of an n-gon is (n−2)180°.
- Similar figures have equal corresponding angles and proportional sides; areas scale by the square of the linear scale factor, and volumes scale by the cube.
- Pythagorean theorem: a²+b²=c² for a right triangle, where c is the hypotenuse. The converse helps classify triangles.
- Circle: circumference C=2πr or πd; area A=πr².
- Volume formulas: prism or cylinder V=Bh; pyramid or cone V=(1/3)Bh; sphere V=(4/3)πr³. Surface area is measured in square units, and volume is measured in cubic units.
Worked example
A right triangle has legs 6 cm and 8 cm. Its hypotenuse is √(6²+8²)=√100=10 cm. A similar triangle has hypotenuse 25 cm, so the linear scale factor is 25/10=2.5. Its legs are 15 cm and 20 cm, and its area is (1/2)(15)(20)=150 cm².
Traps
Do not confuse radius and diameter. Use the perpendicular height, not a slant height, in parallelogram and triangle area formulas. When converting area or volume, square or cube the conversion factor. A scale factor of 2 multiplies lengths by 2 but areas by 4. Check whether a diagram is drawn to scale; never assume it is.