Congurence And Similarity

Congurency:

Congurence And Similarity between triangles

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Two geometric figures are congurent, if they are of the same shape and size.

                                                                                 AB =XY               ∠a = ∠x

BC = YZ               ∠b = ∠y

AC = XZ               ∠c = ∠z

Tests of Congurency:

  • Side Side Side (SSS) – all sides are equal
  • Angle Angle Angle (AAA) – all angles are same
  • Side Angle Side (SAS) – two sides and one angle are equal
  • Right Angled – Hypotenuse – Side – one right angle and hyp & side equal

≡  – To denote “ is congruent to”

≢ – To denote “ is not congruent to”

 

Similarity:

When two figures are similar, they are exactl the same in shape but not in size.

Test:

  • Equal corresponding Angles:

The angles of one triangle are equal to corresponding angles of the other triangle.

Capture71

 

  • Proportional Corresponding Angles.
  • Two Pairs of Proportional Corresponding Sides with equal angles.

We right similarity as ( ~ ) i.e ΔABC ~ ΔDEF

 

Ratios of Area And Volumes:

Same Ratio:

Capture72

Ratio of Area:Capture73

Ratio of Volume:Capture74

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