Answer:
C) [tex]\overline {AD}[/tex] ≅ [tex]\overline {AC}[/tex], [tex]\overline {BD}[/tex] ≅ [tex]\overline {CD}[/tex], [tex]\overline {AD}[/tex] ≅ [tex]\overline {AD}[/tex]
Step-by-step explanation:
From the given diagram, we have;
Segment [tex]\overline {AB}[/tex] in triangle ΔABD is congruent to segment [tex]\overline {AC}[/tex] in triangle ΔACD
Segment [tex]\overline {AD}[/tex] is congruent to segment [tex]\overline {AD}[/tex] by reflexive property
For ΔABD to be congruent to ΔACD, by the Side-Side-Side, SSS, congruency postulate, all the sides of ΔABD should be congruent to the corresponding side of ΔACD, the required added statement is therefore;
Segment [tex]\overline {BD}[/tex] is congruent to segment [tex]\overline {CD}[/tex]
The correct option is therefore option C;
[tex]\overline {AD}[/tex] ≅ [tex]\overline {AD}[/tex], [tex]\overline {BD}[/tex] ≅ [tex]\overline {CD}[/tex], [tex]\overline {AD}[/tex] ≅ [tex]\overline {AC}[/tex]
