Geometry the congruence of triangles

GeometryCongruence Of Triangles

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Congruent TrianglesCongruent triangles have three congruent sides and three congruent angles. However, triangles can be proved congruent without showing 3 pairs of congruent sides and angles.

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LAHALLHLFOR RIGHT TRIANGLES ONLY

AAS ASA SAS

SSSFOR ALL TRIANGLESThe Triangle Congruence Postulates And Theorms

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Example

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Q1. Why arent these triangles congruent? What do we call these triangles?So, how do we prove that triangles are congruent?

ASA (Angle Side Angle)

A D AB DE B E

ABC DEF

BA EDFCAns 1.

AAS (Angle Angle Side)

A D B E BC EF

ABC DEFBAC

EDF

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SSS (Side Side Side)

AB DE BC EF AC DF

ABC DEF

BA C

ED F

SAS (Side Angle Side)

AB DE A D AC DF

ABC DEF

ED

F

BAC

Example 2If two isosceles triangles have a common line segments joining their vertices bisects the common base at right angles.Given TwoABC and DBC with the same base BC, in which AB=AC and DB=DC. Also ,AD meets BC in E.To Prove- BE=CE and AEB= AEC=90*

ABCDE

1234BD

ACE3412

In ABD & ACD, we have :AB=AC (given)DB=DC(given)AD=AD(common)ABD= ACD(SSS criteria)Now, in ABE & ACE, we have:AB=AC (given) AE=AE(common)ABE= ACE (SAS criteria ) BE=CE (.) & 3=4But 3= 4=180*(linear pair)24=180*,i.e.4=90*3=4=90*Hence, BE=CE & AEB =AEC=90*BD

ACE3412

ABCDE

1234THUS PROVED