Darragh says that $|DF|=|EF|$. Explain why he is correct.
Draw in the line segments $[DF]$ and $[EF]$. Now prove, using congruent triangles, that the line $BF$ bise... show full transcript
Worked Solution & Example Answer:Darragh says that $|DF|=|EF|$ - Junior Cycle Mathematics - Question 11 - 2014
Step 1
Darragh says that |DF|=|EF|. Explain why he is correct.
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Answer
The construction lines at the point F represent a fixed distance from D and the same distance from E. Since F is the point of intersection of these lines, the lengths |DF| and |EF| must be the same.
Step 2
Draw in the line segments [DF] and [EF]. Now prove, using congruent triangles, that the line BF bisects \angle ABC.
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Answer
To demonstrate that BF bisects \angle ABC, we first draw the line segments DF and EF. We know by construction that |BD| = |BE| and that |DF| = |EF|. This leads to the two triangles \triangle AFB and \triangle AEB being similar. Therefore, since |EBF| = |F| = |DF|, we conclude that BF bisects \angle ABC.
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