SOLUTION: In the diagram to the bottom, ABCG is a parallelogram, and BF=21cm, FE=9cm. Find the length, in cm, of ED. Diagram: https://imgur.com/a/ohBRyuL

Algebra ->  Length-and-distance -> SOLUTION: In the diagram to the bottom, ABCG is a parallelogram, and BF=21cm, FE=9cm. Find the length, in cm, of ED. Diagram: https://imgur.com/a/ohBRyuL      Log On


   

Question 1149590: In the diagram to the bottom, ABCG is a parallelogram, and BF=21cm, FE=9cm. Find the length, in cm, of ED.
Diagram: https://imgur.com/a/ohBRyuL
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


(1) Triangles AFE and CFB are similar. FE=9 and FB=21 are corresponding parts of those triangles, so the ratio of similarity is 9:21 or 3:7.

(2) So let the lengths of corresponding parts AE and CB be 3x and 7x.

(3) ABCG is a parallelogram; BC = 7x and AE = 3x. Use that to find an expression for the length of EG.

(4) Angles BAG and EGD are congruent because ABCG is a parallelogram. Angles AEB and GED are congruent because they are vertical angles.

(5) So triangles BAE and DGE are similar. Sides AE and EG are corresponding parts of those triangles, giving you the ratio of similarity.

(6) BE and ED are also corresponding parts of those triangles. The length of ED is what you are to find; the length of BE is known from the given information.

(7) Use the ratio of similarity of those two triangles to answer the question.