Segment Addition Postulate: Find AD given BC=6, BD=14, AC=9

Published on May 8, 2026

Geometry

Learn to find the length of AD using the Segment Addition Postulate and the given lengths of segments BC, BD, and AC.

Question

Answer

The problem states that point

is between points

and

, and point

is between points

and

. This means the points are arranged in the order

along a line.

We are given the following lengths:

We need to find the length of

Since

is between

and

, we can write the relationship:

We are given

and

. Substituting these values into the equation:

Subtracting 6 from both sides:

Since

is between

and

, we can write the relationship:

We are given

and

. Substituting these values into the equation:

Subtracting 6 from both sides:

Now we need to find the length of

. Since the points are in the order

, we can express

as the sum of the lengths of the segments:

We have found the lengths of

, and

Substituting these values into the equation for

Alternatively, we know that

and

.
We are given

and

.
Since

is between

and

Since

is between

and

.
We are given

and

The length

can also be expressed as

.
We found

and we are given

The final answer is

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Segment Addition Postulate: Find AD given BC=6, BD=14, AC=9

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