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Geometry Proof : Isosceles Triangle and Bisector

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ABC is an isosceles triangle. M is the midpoint of side BC.
E is a point on AC. The (angle) bisector of angle ABE intersects AM at F.
What is EF?
Prove your Conjecture.

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A proof involving an isosceles triangle and a bisector is provided. The expert proves a conjecture.

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Yes, is the bisector of . The shortest proof is based on the fact that three bisectors must intersect at a unique point. Consider a triangle ABE, BF and AM are bisectors. (NOTE: Am is a bisector of as the triangle ABC is an isosceles triangle and M is the midpoint of side BC). So, the third bisector of the ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
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  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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