Question

Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures.

Answer 1

I understand this much

Answer 2

CBD is proportionate to ACE

Answer 3

And CB is similar to CA, CD is similar to CE

Answer 4

Angle C is common to both of them so we have 3 condition satisfied for congruence and hence both triangle CBD and CAE are congruent and hence opp sides proportionate

Answer 5

Hold on

Answer 6

The three angles of the two triangles are equal to each other. Hence the two triangles are similar and therefore the corresponding sides are proportional