Segmentul AD contine punctele B si C astfel incat AB = 4cm, AC = 12cm, AD = 20cm. Aratati ca punctul C este mijlocul segmentului BD

Here we know a distribution of points and some of the segments that are generated. We want to see if C is the midpoint of segment BD.

So we know that segment AD contains points B and C.

We also know:

From this, we want to find segment BD.

You can look the image at the end, which describes the situation.

In the image is easy to see that segment BD is equal to the difference between AD and AB.

Then we have:

Similarly, we could find any segment we want.

Then we can see that CD is equal to AD - AC, or:

CD = AD - AC = 20cm - 12cm = 8cm

CD = 8cm

Then, BC will be equal to the difference between BD and CD

BC = BD - CD = 16cm - 8cm = 8cm

Then we have:

BC = 8cm = CD

So is easy to see that C is the midpoint of BD, because it "breaks" the segment into two equal halves.

If you want to learn more, you can read:

link

Step-by-step explanation:

If segment AD contains point B and, then A, B, C and D lies on the same straight line as shown in the attachment.

To show that point C is the middle of point BD, we musr show that segment BC is equal to CD i.e BC = CD.

From the diagram, AC = AB+BC

Given AC = 12cm and AB = 4cm

BC = AC-AB

BC = 12cm - 4cm

BC = 8cm

Also AD = AB+BC+CD

Given AD = 20cm, AB = 4cm and BC = 8cm

CD = AD-(AB+BC)

CD = 20-(4+8)

CD = 20-12

CD = 8cm

It can be seen that BC = CD = 8cm, hence C is the midpoint of B and C.

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