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Numerade Educator

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Problem 32 Hard Difficulty

$\overline{D C}$ is a median of $\triangle A B C .$ Which of the following statements is true?
(F) $B C<A C$
(G) $B C>A C$
(H) $A D=D B$
(J) $\triangle D C=A B$

Answer

H

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Video Transcript

talk about a random triangle, ABC and a given median of segment D. C. So the median segment D C would have to start at Point d, the midpoint of a B and go through point C. So that tells us that segment A D is congruent to segment B D because of median starts from a midpoint of one side of a triangle. The question is, which of the four statements is true? Is it possible that BC is less than a C? Well, we don't know that information because we don't know anything about the angle measurements created by the median. We don't know whether the median is also a perpendicular by sector. We don't know whether it creates larger and smaller angles. We don't know anything else about the median, other than the fact that a the definition of a median starts from a midpoint of a segment, so we can't tell whether B C is less than a C. At the same time, we can't tell whether B C is greater than a C. The definition of a median tells us it starts at a midpoint of one side, and if its median d C that means it ends at point C, so it must go through the midpoint of Segment A, be creating to congruent segments or to equal segments 80 being equal to D B. Is it possible for D. C T equal A. B and some circumstances It is possible, but without any other given information. We don't know anything about the lengths of segment. Maybe we don't know anything about the lengths of D. C. So we don't have enough information to prove that they're equal. And other examples. It is possible that these two segments could be equal to each other, but not in this example.

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