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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
30
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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