Screening Paper II · 1 General Mental and Psychological Abilities · APPSC Group 1
1.4.2 Geometry and trigonometry notes
8 notes, in reading order.
- 1.4.2.1Lines, angles and parallel lines
Angle questions run on three sums (90°, 180°, 360°) and three parallel-line rules (corresponding equal, alternate equal, co-interior add to 180°); set up one equation and solve.
Advanced · 6 min · Full course - 1.4.2.2Triangles: angle properties, congruence, similarity and centres
Triangle questions use the 180° angle sum and the exterior-angle rule for angles, the triangle inequality for sides, ratios for similar figures, and four centres whose angle formulas (90 + A/2, 2A, 180 − A) answer most "find ∠BOC" questions.
Advanced · 7 min · Full course - 1.4.2.3Right triangles: Pythagoras, triples and special triangles
In a right triangle the square on the hypotenuse equals the sum of the squares on the legs; knowing the common triples and the 30-60-90 and 45-45-90 ratios turns most questions into one-line answers.
Advanced · 6 min · Full course - 1.4.2.4Quadrilaterals and polygons: angle sums, diagonals and properties
Polygon questions come from two formulas (interior sum (n − 2) × 180°, exterior sum 360°) and the diagonal count n(n − 3)/2; quadrilateral questions come from a short table of which sides, angles and diagonals are equal, parallel or perpendicular.
Advanced · 7 min · Full course - 1.4.2.5Circles: chords, tangents and angle theorems
Circle questions rest on one right triangle (radius, half-chord, distance from the centre), one angle rule (angle at the centre is twice the angle on the circle), the cyclic-quadrilateral 180° rule, and the tangent facts (tangent ⊥ radius, equal tangents from a point).
Advanced · 7 min · Full course - 1.4.2.6Coordinate geometry basics: distance, section formula, slope and area
A handful of formulas (distance, section, centroid, area, slope, distance from a line) answers almost every coordinate question; most can be checked in seconds by sketching the points.
Advanced · 7 min · Full course - 1.4.2.7Trigonometry basics: ratios, standard angles and identities
Learn the six ratios as sides of a right triangle, the value table for 0°, 30°, 45°, 60° and 90°, the three squared identities and the complementary-angle swap; almost every aptitude trigonometry question is one of these in disguise.
Advanced · 6 min · Full course - 1.4.2.8Heights and distances
Draw the right triangle, use tan (height over horizontal distance) at each angle, and remember that 30°, 45° and 60° turn every answer into a multiple of √3 or 1.
Advanced · 7 min · Full course
Practise Geometry and trigonometry. Questions with answers explained, from the same topics.
Medha AI is an independent preparation service. It is not affiliated with, endorsed by or connected to APPSC, TSPSC, MPSC, UPSC or any other commission or government body.