In isosceles triangles the angles at the base are equal to one another, and, if the equal straight lines are produced further, then the angles under the base will be equal to one another.

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Euclid's Elements Book I, Proposition 5

## Friday, February 19, 2010

### Euclid's Elements Book I, Proposition 5: (Pons Asinorum)

Labels:
Book I,
congruence,
Elements,
Euclid,
isosceles,
Pons asinorum,
triangle

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let alpha=a and beta=b.

ReplyDeleteAs ABC is an isosceles triangle ,base angles are congruent.

AB=BC implies angle BAC = angle BCA

hence a=a'...(1)

angle DAC + angle CAB= 180..(angles in a linear pair)

angle ECA + angle BCA= 180..(angles in a linear pair)

Hence,

angle DAC + angle CAB = angle ECA + angle BCA

b + a = a'+ b'

b = a - a'+ b'

b = b'....(by (1))