To solve the questions, I can write easily that
The area of ADC and BDC triangles equal and similarly EBD and CED triangle areas are equal.
From this conditions how to show the following conditions are true or not?
2026-02-24 02:16:35.1771899395
How to prove these conditions right or wrong?
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A. [midpoint theorem]
B. [Equal base and equal altitude]
C. (It is Not necessarily true). When C is obtuse, the foot of the perpendicular from E to AC will lie outside of ⊿ABC. This mean CF is less than 0.5 of AC and AF is then larger than 0.5 of AC. In short, AF > FC. This further implies the claim is not true [according to equal base and equal altitude]. See illustration below.
D. This is not true in general unless AD = DC. Then, AD = DC = DB. This further means angle C must be 90 degrees.
E. This is not true obviously. [Edit: True because area = AC * altitude / 2 = AC * DF.]