Lines, Angles & Triangles
SSC GD Exam Preparation - Quantitative Aptitude
Geometry is a branch of mathematics that deals with shapes, sizes, and properties of figures. In competitive exams, questions often focus on basic properties, formulas, and simple problem-solving.
🔹 1. Lines
Types of Lines:
Parallel Lines
Never meet, same direction
Perpendicular Lines
Intersect at 90°
Intersecting Lines
Cross at any angle except 90°
Properties:
Sum of angles on a straight line = 180°
Vertically opposite angles are equal
🔹 2. Angles
Types of Angles:
Acute Angle
< 90°
Right Angle
= 90°
Obtuse Angle
> 90°
Straight Angle
= 180°
Key Angle Rules:
Sum of angles at a point = 360°
Sum of angles on a straight line = 180°
Sum of angles in a triangle = 180°
Sum of angles in a quadrilateral = 360°
🔹 3. Triangles
Types of Triangles (By Sides):
Equilateral
All sides equal
Isosceles
Two sides equal
Scalene
All sides unequal
Types of Triangles (By Angles):
Acute
All angles < 90°
Right
One angle = 90°
Obtuse
One angle > 90°
Key Formulas:
Perimeter of Triangle: P = a + b + c
Area (Heron's Formula): s = (a+b+c)/2, Area = √[s(s-a)(s-b)(s-c)]
Area (base × height): ½ × base × height
Important Properties:
Sum of angles = 180°
Pythagoras Theorem: a² + b² = c² (Right Triangle)
🧠 Practice Section: 15 Questions (With Answers)
Each Q followed by its Answer (SSC style). Click on "View Answer" to check your understanding.
Q1. Find the 3rd angle of a triangle if two angles are 50° and 60°
View Answer
180 - (50 + 60) = 70°
Q2. A triangle has sides 3, 4, 5. Is it right-angled?
View Answer
Yes, 3² + 4² = 5² ⇒ 9 + 16 = 25
Q3. Sum of angles on a straight line = ?
View Answer
180°
Q4. Vertically opposite angles are:
View Answer
Equal
Q5. If one angle of a triangle is 90° and another is 30°, find the 3rd angle
View Answer
180 - 90 - 30 = 60°
Q6. Length of hypotenuse in a right triangle with sides 6 and 8
View Answer
√(6² + 8²) = √(36 + 64) = √100 = 10
Q7. Area of triangle with base 10 and height 6
View Answer
½ × 10 × 6 = 30
Q8. Sum of angles in a quadrilateral
View Answer
360°
Q9. Two parallel lines are cut by a transversal. Alternate angles are:
View Answer
Equal
Q10. Perimeter of triangle with sides 5, 7, 8
View Answer
5 + 7 + 8 = 20
Q11. Area of triangle using Heron's formula with sides 3, 4, 5
View Answer
s = (3+4+5)/2 = 6, Area = √[6(6-3)(6-4)(6-5)] = √[6×3×2×1] = √36 = 6
Q12. Type of triangle with angles 60°, 60°, 60°
View Answer
Equilateral & Acute
Q13. Find missing angle if angles are in ratio 2:3:4
View Answer
Sum = 180, let angles = 2x,3x,4x → 9x=180 → x=20 → angles = 40°, 60°, 80°
Q14. If a triangle has sides 7, 24, 25, is it right-angled?
View Answer
Yes, 7² + 24² = 49 + 576 = 625 = 25²
Q15. In a right triangle, if one angle is 45°, find the other acute angle
View Answer
90 - 45 = 45°
✅ SSC GD Exam Strategy
🟢 Memorize all angle properties and triangle types
🟢 Practice Pythagoras theorem applications
🟢 Master Heron's formula for area calculations
🟢 Learn to identify triangle types quickly
🟢 Time yourself - aim for 30-45 seconds per geometry problem
You've completed Geometry: Lines, Angles & Triangles!
SSC GD Tip: Mastering basic geometry concepts is essential for solving spatial reasoning problems efficiently. Remember the fundamental angle properties, triangle classifications, and key formulas like Pythagoras theorem and Heron's formula. Regular practice with previous year SSC GD questions will build your speed and accuracy. Pay special attention to right triangles and angle calculation problems as they frequently appear in exams. Visualizing the geometric figures can help you solve problems faster and more accurately.
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