1
$\begingroup$

Let A1A2A3 ....A9 be a nine-sided regular polygon with side length 2 units. The difference between the lengths of the diagonals A1A5 and A2A4 equals $2$.

I can prove it very easily if I could have proved that the side $A_2 A_4$ is parallel to $A_1 A_5$ in the following picture.enter image description here

Is it possible to prove?

$\endgroup$
1
  • $\begingroup$ The figure you drew has ten sides. $\endgroup$ Nov 20 '19 at 12:05
2
$\begingroup$

Yes. $\angle415\cong\angle142$, since they are inscribed angles that intercept congruent arcs of $\frac{360^\circ}9$. Since those angles are alternate interior angles of the lines $\overline{24}$ and $\overline{15}$ cut by transversal $\overline{14}$, we conclude that $\overline{24}\parallel\overline{15}$.

$\endgroup$
3
  • $\begingroup$ Can you please edit your answer? I think there are some printing mistakes..@Matthew Daly $\endgroup$
    – sani
    Nov 20 '19 at 12:06
  • $\begingroup$ @sani What printing mistakes are you referring to? I don't see anything wrong with it. $\endgroup$
    – user694818
    Nov 20 '19 at 12:08
  • $\begingroup$ Yea I misunderstood..@Matthew Daly $\endgroup$
    – sani
    Nov 20 '19 at 12:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.