Question 1209159: In the diagram, ABCG is a parallelogram, and BF = 18 cm, FE = 6 cm. Find the length, in cm, of ED.
https://ibb.co/GCZMVZF
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Angles AEF and CBF are congruent (parallel lines cut by a transversal).
Likewise angles EAF and BCF are congruent.
So triangles AEF and CBF are similar; and legs EF and BF, for which lengths are given, are corresponding parts of those similar triangles.
Since those lengths are 18 and 6, the ratio of similarity between the two triangles is 3:1.
That means BC is 3 times the length of AE; and that means EG is twice the length of AE.
Angles BAG and AGC are supplementary (adjacent angles in parallelogram ABCG), so angles AGD and BAE are congruent.
That makes triangles BAE and DGE similar; and with EG twice AE, the ratio of similarity between those two triangles is 2:1.
And BE, with length 18+6=24, and ED are corresponding parts of those two triangles, so the length of ED is twice the length of BE, or 2*24 = 48.
ANSWER: 48
|
|
|
