Solve the problem. Given: KW = 16 cm, KO = 8 cm, OD = DW. Find: OD, DW.

Solution:

We are given a line segment KW with points O and D on it. We know that KW = 16 cm and KO = 8 cm. We are also given that OD = DW.

First, let's find the length of the segment OW.

Since O is between K and W, we have KW = KO + OW.

16 cm = 8 cm + OW.

OW = 16 cm - 8 cm = 8 cm.

Now we know that OW = 8 cm. We are also given that OD = DW, and O, D, W are points on the line segment in that order. Therefore, OW is the sum of OD and DW.

OW = OD + DW.

Since OD = DW, we can write:

OW = OD + OD = 2 * OD.

8 cm = 2 * OD.

OD = 8 cm / 2 = 4 cm.

Since OD = DW, then DW = 4 cm.

Verification:

KO = 8 cm, OD = 4 cm, DW = 4 cm.

KW = KO + OD + DW = 8 cm + 4 cm + 4 cm = 16 cm. This matches the given information.

Also, OD = 4 cm and DW = 4 cm, so OD = DW is true.

Final Answer:

OD = 4 cm, DW = 4 cm.