Question

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

Answer 1

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.