we have that
If GC bsect each other
then
AH=HD
and
If AD bisect each other
then
GH=HC
so
m by vertical angles
therefore
triangle GHA is congruent with triangle CHD by SAS theorem
1 AD and GC bisect each other--------> given
2. AH=HD ------> by GC bisect each other
3. GH=HC -----> by ASD bisect each other
4. m by vertical angles
5. riangle GHA is congruent with triangle CHD ------> by SAS theorem congruence