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BOOK I. PROP. V. THEOR.
5
N any isosceles triangle
if the equal sides be produced, the external angles at the base are equal, and the internal angles at the base are also equal.
![](http://upload.wikimedia.org/wikipedia/commons/2/2c/Byrne_39_diagram.png)
Produce , and
(post. 2.), take
=
, (pr. 3.); draw
and
.
Then in and
we have,
=
(const.),
common to both, and
=
(hyp.) ∴
=
,
=
and
=
(pr. 4.).
Again in and
, we have
=
, ∴
=
and
=
(pr. 4.) but
=
, ∴
=
(ax. 3.)
Q.E.D.