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D ,\ E ,\ F are the mid-point of the s...

`D ,\ E ,\ F` are the mid-point of the sides `B C ,\ C A\ a n d\ A B` respectively of ` A B Cdot` Then ` D E F` is congruent to triangle. `A B C` (b) AEF (c) `B F D ,\ C D E` (d) `A F E ,\ B F D ,\ C D E`
Given : D, E, F are the mid-point of the sides BC, CA and AB .

Text Solution

Verified by Experts

Solution : `FE=BD`(mid-point theorem)
`CD=DB`(since D is the midpoint of BC)
Now in `triangles AFE and DEF`
FE is common in both the triangles
`DF=AE`(from the mid-point theorem)
`DE=AF`(from the mid-point theorem)
This shows that triangles DEF and AFE are congruent to each other by SSS congruence.
Triangles DEF and BFD are also congruent to each other by SSS congruence.
` triangles DEF and CDE` can be shown congruent to each other in a similar way by SSS congruence.
Hence , option (d) is correct.
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