Geometry
What to know
Candidates should compute perimeter, area, and volume for common figures: rectangles, triangles, parallelograms, trapezoids, circles, and rectangular solids. Know angle relationships-complementary (90°), supplementary (180°), vertical angles, and angles formed by parallel lines cut by a transversal. The Pythagorean theorem and the coordinate plane (distance, midpoint, transformations) are core. Familiarity with similar figures and scale factors is expected.
Traps to watch
- Area of a triangle is half the base times height, and height must be perpendicular to the base-not a slanted side.
- Radius versus diameter: use r, not d, in area and circumference formulas.
- Similar figures have equal angles and proportional sides; equal areas do not follow from equal angles.
- The Pythagorean theorem applies only to right triangles, and c is always the hypotenuse.
- Watch units: perimeter is linear, area is squared, volume is cubed.
Worked example
A right triangle has legs 6 cm and 8 cm. The hypotenuse is √(6² + 8²) = √(36 + 64) = √100 = 10 cm. Its area is ½ × 6 × 8 = 24 cm².
Rule of thumb
Sketch and label the figure, mark known angles and lengths, then choose the formula that matches the given information. Check that units are consistent before computing.