Geometry
About 6 min · Quantitative Ability · English
Time worked out from the lesson's 369 words at 150 words a minute, plus a minute for each question.
Geometry is part of the Quantitative Ability section in HSSC CET. Questions typically test your understanding of basic properties of lines, angles, triangles, quadrilaterals, and circles.
Key ideas
- Angle relationships: Complementary angles sum to 90°, supplementary angles sum to 180°. Vertically opposite angles are always equal.
- Parallel lines with transversal: When a transversal cuts two parallel lines, alternate interior angles are equal, corresponding angles are equal, and co-interior (same-side interior) angles are supplementary.
- Triangle angle sum: Interior angles of any triangle add up to 180°. Exterior angle equals the sum of the two non-adjacent interior angles.
- Triangle inequality: The sum of any two sides must be greater than the third side. The difference of any two sides must be less than the third side.
- Congruence and similarity: Congruent triangles are identical in shape and size (SSS, SAS, ASA, RHS). Similar triangles have equal angles and proportional sides (AA, SSS ratio, SAS ratio).
Watch out for
- Applying Pythagoras to non-right triangles → Always verify that one angle is 90° before using a² + b² = c². For other triangles, use cosine rule or Heron's formula.
- Confusing similar and congruent triangles → Similar triangles have proportional sides (not equal). Congruent triangles have equal corresponding sides. Ratios of areas of similar triangles = (ratio of sides)².
- Forgetting units in circle problems → When radius is in cm and answer choices are in m (or vice versa), convert carefully. Also note whether question asks for radius or diameter.
Quick reference
- Triangle angles sum to 180°; quadrilateral angles sum to 360°.
- Exterior angle of triangle = sum of two opposite interior angles.
- Pythagorean triplets to memorise: 3-4-5, 5-12-13, 8-15-17.
- Tangent ⊥ radius; two tangents from external point are equal.
- Rhombus area = (1/2) × product of diagonals.
Check yourself: 3 questions
1. In a triangle ABC, angle A = 50° and angle B = 60°. What is the measure of angle C?
2. Two parallel lines are cut by a transversal. If one of the alternate interior angles is 75°, what is the measure of its alternate interior angle?
3. The sum of two angles of a quadrilateral is 180° and the other two angles are equal. Find the measure of each of the equal angles.
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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