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Numerade Educator



Problem 27 Hard Difficulty

Make a conclusion based on the Hinge Theorem or its converse. (Hint: Draw a sketch.)
In $\triangle X Y Z, \overline{X M}$ is the median to $\overline{Y Z}$, and $Y X>Z X$.


$$m \angle Y M X>m<\lambda M X$$


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Video Transcript

Let's draw a triangle X y Z with the given information and let's see what we can conclude. So let's start with Triangle X y Z given segment X m is the median two y z that's two y Z. That means this point has to be point em. It's also a midpoint of segment y Z because the definition of a median is a segment that goes from a midpoint of one side to the vertex of the opposites opposite of the side. So point M is a midpoint of y Z. We also know that segment why X is greater than segment Z X. So why X I'm gonna mark that twice is greater than Z X and I'm gonna mark that once. What we do know is X M is congruent to itself. So based on the converse of the hinge here, um, we have two sides that are corresponding and congruent. We've got segment y m and segment Z m are congruent to each other. We have segment X m is congrats to itself. So we must be focused on the included angle of those sides. And if why X is greater than Z X by the converse hinge. There we can conclude the angle opposite of the longer side has to be your larger angle. So the measurement of angle why I m X is going to be greater than the angle opposite of our shorter side, which is the measurement of angle Z m X, using the converse of the hinge there.

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