Question

1. & 2. In the diagram below, points A, B, and C are collinear. Answer each of the following questions. The figure shown below is not drawn to scale, meaning you cannot determine your answers by using your ruler.​

Answer 1

a)
`\overline{AB}` = 8 in

b) When the length of AC =
`6(1)/(2)` in. and BC =
`3(1)/(2)` in.
`\overline{AB}` = 10 in

c) When the length of AB = 10.2 in. and BC = 3.7 in.
`\overline {AC}` = 6.5 in

d) When the length of AB =
`4(3)/(4)` in. and BC =
`3(1)/(4)` in. in.
`\overline {BC}` =
`1(1)/(2)` in

Explanation:

a) When the length of AC = 5 in. and CB = 3 in. we have;

The length of
`\overline {AB}` = AC + CB (segment addition postulate)

Therefore;

`\overline{AB}` = 5 in. + 3 in. = 8 in.

b) When the length of AC =
`6(1)/(2)` in. and BC =
`3(1)/(2)` in. we have;

The length of
`\overline {AB}` = AC + CB (segment addition postulate)

Therefore;

`\overline{AB}` =
`6(1)/(2)` in.+
`3(1)/(2)` in. = 10 in.

c) When the length of AB = 10.2 in. and BC = 3.7 in. we have;

The length of
`\overline {AC}` = AB - BC (converse of the segment addition postulate)

Therefore;

`\overline {AC}` = 10.2 in.+ 3.7 in. = 6.5 in.

d) When the length of AB =
`4(3)/(4)` in. and BC =
`3(1)/(4)` in. in. we have;

The length of
`\overline {BC}` = AB - AC (converse of the segment addition postulate)

Therefore;

`\overline {BC}` =
`4(3)/(4)` in. -
`3(1)/(4)` in.=
`1(1)/(2)` in.