Geometry
About 6 min · Mathematics and Science (Paper II) · English
Time worked out from the lesson's 398 words at 150 words a minute, plus a minute for each question.
Geometry is part of the Mathematics section in AP TET Paper II, testing both content knowledge and the ability to apply geometric principles to solve problems. This topic covers the properties and relationships of two-dimensional shapes (triangles, quadrilaterals, circles) along with coordinate geometry and basic trigonometry—though coordinate geometry (distance and section formulas) and trigonometric ratios are Class 10 topics, beyond the Classes 6–8 curriculum.
Key ideas
- Triangle classification: Triangles are classified by sides (scalene, isosceles, equilateral) and by angles (acute, right, obtuse). The angle sum property states that interior angles always total 180°.
- Congruence and similarity: Two triangles are congruent if they have identical shape and size (SSS, SAS, ASA, AAS, RHS criteria). Similar triangles have proportional sides and equal corresponding angles (AA, SSS, SAS similarity).
- Quadrilateral hierarchy: Quadrilaterals include parallelograms, rectangles, squares, rhombuses, and trapeziums. Each has specific properties regarding sides, angles, and diagonals. Angle sum of any quadrilateral is 360°.
- Circle terminology: Key terms include radius, diameter, chord, arc, sector, segment, tangent, and secant. A tangent touches the circle at exactly one point and is perpendicular to the radius at that point.
- Coordinate geometry basics: The Cartesian plane uses ordered pairs (x, y) to locate points. Distance and section formulas help find lengths and divide line segments in given ratios.
Watch out for
- Confusing congruence criteria → SSA (Side-Side-Angle) is NOT a valid congruence criterion; only RHS works for right triangles with hypotenuse and one side.
- Forgetting to halve in area formulas → Triangle area and rhombus area formulas include (1/2); students often omit this factor under time pressure.
- Mixing up sin and cos values → Remember: sin increases from 0° to 90° (0 to 1), while cos decreases (1 to 0). Use the mnemonic: "sin starts small."
Quick reference
- Triangle angle sum = 180°; Quadrilateral angle sum = 360°
- Pythagoras: c² = a² + b² (right triangle only)
- Distance between (x₁,y₁) and (x₂,y₂) = √[(x₂−x₁)² + (y₂−y₁)²]
- sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2
- Tangent ⊥ radius at point of contact
Check yourself: 3 questions
1. In triangle ABC, angle A = 50° and angle B = 60°. What is the measure of angle C?
2. A circle has a radius of 7 cm. What is the length of its diameter?
3. In a parallelogram ABCD, if angle A = 70°, what is the measure of angle C?
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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