Answer:
a) [tex]\overline{AB}[/tex] = 8 in
b) When the length of AC = [tex]6\frac{1}{2}[/tex] in. and BC = [tex]3\frac{1}{2}[/tex] in. [tex]\overline{AB}[/tex] = 10 in
c) When the length of AB = 10.2 in. and BC = 3.7 in. [tex]\overline {AC}[/tex] = 6.5 in
d) When the length of AB = [tex]4\frac{3}{4}[/tex] in. and BC = [tex]3\frac{1}{4}[/tex] in. in. [tex]\overline {BC}[/tex] = [tex]1\frac{1}{2}[/tex] in
Step-by-step explanation:
a) When the length of AC = 5 in. and CB = 3 in. we have;
The length of [tex]\overline {AB}[/tex] = AC + CB (segment addition postulate)
Therefore;
[tex]\overline{AB}[/tex] = 5 in. + 3 in. = 8 in.
b) When the length of AC = [tex]6\frac{1}{2}[/tex] in. and BC = [tex]3\frac{1}{2}[/tex] in. we have;
The length of [tex]\overline {AB}[/tex] = AC + CB (segment addition postulate)
Therefore;
[tex]\overline{AB}[/tex] = [tex]6\frac{1}{2}[/tex] in.+ [tex]3\frac{1}{2}[/tex] in. = 10 in.
c) When the length of AB = 10.2 in. and BC = 3.7 in. we have;
The length of [tex]\overline {AC}[/tex] = AB - BC (converse of the segment addition postulate)
Therefore;
[tex]\overline {AC}[/tex] = 10.2 in.+ 3.7 in. = 6.5 in.
d) When the length of AB = [tex]4\frac{3}{4}[/tex] in. and BC = [tex]3\frac{1}{4}[/tex] in. in. we have;
The length of [tex]\overline {BC}[/tex] = AB - AC (converse of the segment addition postulate)
Therefore;
[tex]\overline {BC}[/tex] = [tex]4\frac{3}{4}[/tex] in. - [tex]3\frac{1}{4}[/tex] in.= [tex]1\frac{1}{2}[/tex] in.
