CK12 - Geometry

2. Assume is equilateral.Thenby definition,the sidesare congruent.By the parallelpostulate,

we can constructa line parallelto the basethroughpoint as follows:

Fromthis we can showwith alternateinterioranglesthat the triangleis equiangularso = =

. This contradictsthe givenstatementthat.
3. Assumethat is not greaterthan. Theneither in whichcase , whichis a contradiction,

or , in whichcasewe can solvethe quadraticinequalityto get , also a contradiction

of the fact that.

4. Assumethat the linesare not parallel.Then. But = for verticalangles,so

we have. This is a contradictionof the fact that.

5. Hint: This is theorem5-11.


6. Assume , say. By Theorem5-11 we have , which
   contradictsthe fact that we havean isoscelestriangle.