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Quantitative Aptitude›Ch 4: Algebra, Geometry & Mensuration›Lines, Angles and Triangles

4.4

Lines, Angles and Triangles

5 min

Mastering fundamental geometry for competitive excellence.

1

The Golden Rule of Triangles

The sum of all interior angles in a triangle is exactly 180 degrees. Congruent triangles are identical in size and shape, while similar triangles have proportional sides.

2

Why Study This?

  • High weightage in SSC CGL, CHSL and Railway NTPC exams.
  • Forms the basis for Height & Distance and Trigonometry.
  • Direct application in Mensuration 2D problems.

Memory Hooks

  • Centroid: Medians meet and divide in 2:1 ratio.
  • Pythagoras: 3-4-5 and 5-12-13 are common exam triplets.
  • Sum of any two sides > Third side always.
3

Important Triangle Centers

CenterFormed ByKey Property
CentroidMedians2:1 ratio
IncentreAngle BisectorsIncircle center
OrthocentreAltitudes90 deg meet
4

Visual Geometry Concepts

SSS Rule

(Three sides match)

SSS Rule: Three sides match

Three sides match

Triangles are congruent.

2:1 Ratio

(Centroid Split)

2:1 Ratio: Centroid Split

Centroid Split

Constitution[ PART IS ]

Top part is double.

Pythagoras

(Right Angle)

Pythagoras: Right Angleabr

Right Angle

H square = P^2 + B^2.

Similarity

(Same Shape)

Similarity: Same Shape

Same Shape

Sides are proportional.

5

Common Exam Traps

AAA proves congruenceAAA only proves similarity

Two triangles with same angles can have different sizes.

Area ratio equals side ratioArea ratio is side ratio squared

If side ratio is 2:3, area ratio is 4:9.

Median bisects the angleMedian bisects the opposite side

Only in equilateral triangles does it bisect the angle.

6

Practice Questions

Q1.If two angles of a triangle are 55 and 65 degrees, what is the third angle?

Q2.The sides of two similar triangles are in ratio 4:5. Find the ratio of their areas.

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