Geometry is the part of SSC CGL Quant that scares students the most — but it shouldn't. SSC geometry is not creative problem-solving; it is the same 15 to 20 standard facts, tested in the same ways, year after year. If you know the facts cold, the questions solve themselves.
This chapter walks through every geometry family in the official SSC syllabus: lines and angles, triangle properties, congruence and similarity, Pythagoras, circles with their chords and tangents, quadrilaterals, and a touch of coordinate geometry. Each concept keeps the facts you actually need and drops the clutter.
The examples are worked exactly the way you should solve them in the exam — name the rule first, then apply it. That habit is what turns geometry from a guessing game into reliable marks.
A straight line makes 180 degrees. When two lines cross, opposite angles (vertical angles) are equal. When a line cuts two parallel lines, alternate interior angles are equal and interior angles on the same side add to 180 degrees. Almost every geometry question starts here — if two lines look parallel in the figure, check which angles that gives you.
Formulas:
The three interior angles of any triangle add to 180 degrees. If you extend one side, the angle formed outside equals the sum of the two interior angles not next to it. The exterior angle is also the supplement of the adjacent interior angle — both routes give the same answer, so use whichever is faster.
Formulas:
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. SSC loves the standard triplets: (3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17) and their multiples. Spotting 6-8-10 as a doubled 3-4-5 saves you a square-root step entirely.
Formulas:
Two triangles are congruent when they are identical — SSS (three sides), SAS (two sides and the included angle), ASA (two angles and the included side), or RHS (right triangle with hypotenuse and one side). They are similar when their angles match but sizes differ: corresponding sides are in the same ratio, and their areas are in the ratio of the SQUARE of the sides. Mixing these two up costs marks: congruent sides are equal, similar sides are proportional.
Formulas:
The angle at the centre is twice the angle at the circumference standing on the same chord. Angles in the same segment are equal. An angle in a semicircle is always a right angle. For tangents: a tangent touches the circle at exactly one point and is perpendicular to the radius there; the two tangents drawn from one external point are equal in length.
Formulas:
A quadrilateral's four interior angles add to 360 degrees. In a parallelogram, opposite sides and opposite angles are equal, and the diagonals bisect each other. A rhombus is a parallelogram with all sides equal and diagonals that bisect at 90 degrees. A rectangle's diagonals are equal. A cyclic quadrilateral — one with all four corners on a circle — has opposite angles adding to 180 degrees, the single most-asked quadrilateral fact.
Formulas:
SSC sometimes asks for the distance between two points or the length of a line segment in coordinate form. Plot the points if you like, but the distance formula does the job directly: subtract the x's, subtract the y's, square both, add, and take the square root. The midpoint of the segment is just the average of the coordinates.
Formulas:
Answer: 110 degrees
Answer: 10 cm
Answer: 100 degrees
Answer: 12 cm
Answer: 12 cm
Answer: 80 degrees
2x + 3x + 4x = 9x = 180, so x = 20. Largest angle = 4 x 20 = 80 degrees.
Answer: 13 cm
Hypotenuse = sqrt(5^2 + 12^2) = sqrt(169) = 13 cm.
Answer: 70 degrees
Opposite angles of a cyclic quadrilateral sum to 180: angle C = 180 - 110 = 70 degrees.
Answer: 15 cm
Tangent^2 = 17^2 - 8^2 = 289 - 64 = 225; tangent = 15 cm.
Answer: 10 units
Distance = sqrt((8-2)^2 + (11-3)^2) = sqrt(36 + 64) = sqrt(100) = 10.
Circles (tangents, cyclic quadrilaterals, centre-vs-circumference angles) and triangles (Pythagoras, similarity) dominate. The official syllabus specifically names triangle centres, congruence and similarity, and common tangents to two or more circles — revise those directly.
Usually yes, but in 2-3 questions — centres, circumradius/inradius and altitude-median relations are frequent enough to matter. The orthocentre (intersection of altitudes), circumcentre (intersection of perpendicular bisectors) and centroid (intersection of medians) are the ones SSC asks about.
Look for equal radii first: any segment from the centre to the circle is the same length. Then check for right angles — tangent-perpendicular-to-radius and angle-in-a-semicircle create the right triangles that unlock most circle questions.
Angles in the same segment are equal, not double — doubling applies to the CENTRE angle vs the circumference angle. Saying the circumference angle is 60 degrees when the centre angle is 60 degrees (instead of 30) is a classic trap.