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.
Click the figure bellow to see the illustration.
Read more at:
Euclid's Elements Book I, Proposition 5
Friday, February 19, 2010
Euclid's Elements Book I, Proposition 5: (Pons Asinorum)
Subscribe to:
Post Comments (Atom)
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))