Question 1171681: given triangle AKC is isoceles with segment KA is congruent to KC
segment KB bisects angle AKC
prove that angle A is congruent to angle C
Answer by ikleyn(52817)   (Show Source):
You can put this solution on YOUR website! .
Compare triangles AKC and CKA (the order of vertices is IMPORTANT (!) ).
These triangles have two pairs of congruent sides:
the side AK of triangle AKC is congruent to side CK of triangle CKA,
and
the side CK of triangle AKC is congruent to side AK of triangle CKA.
In addition, these triangles have common angle K between these pairs of sides.
THEREFORE, according to SAS-test, these triangles are congruent.
Hence, their corresponding angles A and C are congruent.
At this point, the proof is completed.
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