Solve the equation $x+4=10$ and state Euclid's axiom used.

In the given figure, if $AB=CD$, then prove that $\mathrm{AC}=\mathrm{BD}$. Also, write Euclid's axiom used for proving it.

In the given figure, if $PQ=QR=RS$ then prove that $PQ=\frac{1}{3}PS$.

In the given figure, if $\mathrm{AB}=\mathrm{AD}$ and $\mathrm{AC}=\mathrm{AD}$, then prove that $\mathrm{AB}=\mathrm{AC}$. State Euclid's axiom to support this.