Suppose given a trapezoid abcd with bases bc=5 and ad=8, and leg cd=3. the lines ab and cd meet at a point p. find dp

8 units

Step-by-step explanation:

Consider triangles BPC and APD. These two triangles are similar, because

Then, by AA theorem,

Similar triangles have proportional sides lengths:

The last proportion gives you

Then

Using the theorem of similar triangles and applying the knowledge of proportion, the length of segment DP in the diagram given is: 8 units.

See attachment for the diagram of the trapezium that is given.

Applying proportion and the theorem for similar triangles, we will solve for the length of segment DP.

Given:

BC = 5

AD = 8

CD = 3

Note: are similar triangles, therefore, their side lengths will be proportional to each other.

Thus:

To find DP, use

CP = 5

Find DP:

DP = CD + CP

DP = 3 + 5

DP = 8 units

Therefore, using the theorem of similar triangles and applying the knowledge of proportion, the length of segment DP in the diagram given is: 8 units.

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