Answer:
[tex]\overline {AD}[/tex] = 5
Step-by-step explanation:
From the given diagram we are required to find the length of [tex]\overline {AD}[/tex]
The given parameters are;
ΔABC and ΔCDA are congruent
The length of [tex]\overline {BC}[/tex] = 5
The length of [tex]\overline {AC}[/tex] = 7
The length of [tex]\overline {CD}[/tex] = 4
From ΔABC ≅ ΔCDA, we have;
[tex]\overline {AC}[/tex] = [tex]\overline {AC}[/tex] By reflexive property
∴ [tex]\overline {BC}[/tex] = 5 is either equal to [tex]\overline {AD}[/tex] or [tex]\overline {CD}[/tex]
However, [tex]\overline {CD}[/tex] = 4, therefore, [tex]\overline {BC}[/tex] ≠ [tex]\overline {CD}[/tex]
We can then have;
[tex]\overline {BC}[/tex] = [tex]\overline {AD}[/tex] = 5.
