Let ABC be a triangle, and DE parallel to the base BC. Suppose point F is any point onDE. Show that shaded area is less than or equal to one-fourthof the area of the entire triangle. Where α(BDF) + α(CEF) = 14α(ABC) if and only ifpoints D and E are the midpoints of AB and AC, respectively. 23.4 Let ABC be any triangle, let DE be aline parallel to the base, and let F beany point on DE. Show that the area ofthe union of the two triangles DBF andECF is less than or equal to one-fourththe area of the whole triangle, withequality if and only if D and E are themidpoints of AB and AC.BDAFEEC

Answered: Image /qna-images/answer/db48e2ba-0bb4-46d6-978e-ada5a302a4a0.jpg

Let ABC be a triangle, and DE parallel to the base BC. Suppose point F is any point on DE. Show that shaded area is less than or equal to one-fourth of the area of the entire triangle. Where α(BDF) + α(CEF) = 1 4α(ABC) if and only if points D and E are the midpoints of AB and AC, respectively.

Let ABC be a triangle, and DE parallel to the base BC. Suppose point F is any point on DE. Show that shaded area is less than or equal to one-fourth of the area of the entire triangle. Where α(BDF) + α(CEF) = 1 4α(ABC) if and only if points D and E are the midpoints of AB and AC, respectively.

Elementary Geometry for College Students

6th Edition

ISBN:9781285195698

Author:Daniel C. Alexander, Geralyn M. Koeberlein

Publisher:Daniel C. Alexander, Geralyn M. Koeberlein

Chapter10: Analytic Geometry

Section10.4: Analytic Proofs

Problem 30E: Complete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b,...

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Question

Let ABC be a triangle, and DE parallel to the base BC. Suppose point F is any point on
DE. Show that shaded area is less than or equal to one-fourth
of the area of the entire triangle. Where α(BDF) + α(CEF) = 1
4α(ABC) if and only if
points D and E are the midpoints of AB and AC, respectively.

23.4 Let ABC be any triangle, let DE be a
line parallel to the base, and let F be
any point on DE. Show that the area of
the union of the two triangles DBF and
ECF is less than or equal to one-fourth
the area of the whole triangle, with
equality if and only if D and E are the
midpoints of AB and AC.
B
D
A
F
E
E
C

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