Basic Theorems
SSC GD Exam Preparation - Quantitative Aptitude
Basic theorems form the foundation for solving lines, angles, triangles, and quadrilaterals problems in competitive exams. Focus is on key properties, proofs, and problem-solving.
🔹 1. Triangle Theorems
1. Pythagoras Theorem
In a right-angled triangle:
(Hypotenuse)² = (Base)² + (Perpendicular)²
2. Triangle Angle Sum
Sum of angles in a triangle = 180°
3. Exterior Angle Theorem
Exterior angle = Sum of opposite interior angles
4. Midpoint Theorem
Line joining midpoints of two sides is parallel to third side and half its length
🔹 2. Quadrilateral Theorems
1. Parallelogram Properties
Opposite sides are equal
Opposite angles are equal
Diagonals bisect each other
2. Rectangle & Square
All angles = 90°
Diagonals are equal
Diagonals bisect each other
3. Rhombus & Kite
Diagonals are perpendicular
Diagonals bisect opposite angles (rhombus)
🔹 3. Circle Theorems
1. Angle at Centre
Angle at center = 2 × angle at circumference
2. Tangent Theorem
Tangent ⊥ radius at point of contact
3. Cyclic Quadrilateral
Opposite angles sum to 180°
🧠 Practice Section: 15 Questions (With Answers)
Each Q followed by its Answer (SSC style). Click on "View Answer" to check your understanding.
Q1. A right-angled triangle has base 6 cm and height 8 cm. Find hypotenuse.
View Answer
c² = 6² + 8² = 36 + 64 = 100 ⇒ c = 10 cm
Q2. Sum of angles of a triangle?
View Answer
180°
Q3. One angle of a triangle is 70° and another is 50°. Find the third angle.
View Answer
180 - (70 + 50) = 60°
Q4. Exterior angle of a triangle is 120°, find sum of opposite interior angles.
View Answer
120° (Exterior = Sum of opposite interior angles)
Q5. Line joins midpoints of two sides of triangle; third side = 10 cm. Find line length.
View Answer
5 cm (Half of third side, parallel)
Q6. Opposite sides of parallelogram = 12 cm & 8 cm. Find perimeter.
View Answer
2(12 + 8) = 40 cm
Q7. Diagonals of rectangle = 13 cm. Find each side if length = 5 cm.
View Answer
Width = √(13² - 5²) = √(169 - 25) = √144 = 12 cm
Q8. Diagonals of rhombus = 10 cm & 24 cm. Find area.
View Answer
A = ½ × d₁ × d₂ = ½ × 10 × 24 = 120 cm²
Q9. Opposite angles of cyclic quadrilateral = 70°. Find other angles.
View Answer
180 - 70 = 110°
Q10. Angle at center = 100°, find angle at circumference on same arc.
View Answer
100/2 = 50°
Q11. Tangent meets radius at point. Angle between them?
View Answer
90°
Q12. Square with side 6 cm. Find diagonal.
View Answer
d = a√2 = 6√2 ≈ 8.49 cm
Q13. Diagonal of rectangle bisect each other. True or False?
View Answer
True
Q14. In parallelogram, one angle = 70°. Find adjacent angle.
View Answer
110° (Sum of adjacent angles = 180°)
Q15. Rhombus diagonals = 12 cm & 16 cm. Find length of one side.
View Answer
Side = √((12/2)² + (16/2)²) = √(36 + 64) = √100 = 10 cm
✅ SSC GD Exam Strategy
🟢 Memorize all triangle theorems (Pythagoras, angle sum, exterior angle)
🟢 Practice quadrilateral properties for quick identification
🟢 Master circle theorems for angle calculations
🟢 Learn to apply midpoint theorem in triangle problems
🟢 Time yourself - aim for 20-35 seconds per theorem problem
You've completed Geometry: Basic Theorems!
SSC GD Tip: Mastering basic geometry theorems is crucial for solving complex problems efficiently. Remember that theorems provide the logical foundation for geometric proofs and calculations. Regular practice with previous year SSC GD questions will help you recognize which theorem to apply in different scenarios. Pay special attention to Pythagoras theorem, angle properties, and quadrilateral characteristics as they frequently appear in exams. Understanding these theorems will not only help you solve problems faster but also build a strong foundation for advanced geometry concepts.
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