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Numerade Educator

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Problem 2 Easy Difficulty

Compare the given measures.
(FIGURE CANNOT COPY)
$\mathrm{m} \angle S R T$ and $\mathrm{m} \angle Q R T$

Answer

$m \angle S R T>m \angle Q R T$

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Video Transcript

So in this diagram, if I compared angle S r t to angle Q R T. I can see that segment Q R and segment s are corresponding to each other in the notation of the angles. You can actually see that they do correspond in the same order. Also, we've got the reflexive line. R T is congruent to itself Well, the converse hinge there, Um, States, if you have two triangles that have two sides corresponding and congruent, However, the third side of the triangle is not Congrats it to the third side of the second triangle. Then we can go back and compare the angles in triangle cure T. You can see that the side opposite of angle cure T is smaller than the side opposite of angle SRT. And because the sides opposite of these angles are not congruent, then the angles themselves were not congruent the converse of the hinge There, um, states that the smaller side is going to be opposite of the smaller ankle and the larger side is going to be opposite of the larger angle of the two triangles. Therefore, we can say the measurement of angle cure t his opposite of side measurement three. So it is less than the measurement of Angle SRT because Angle SRT is opposite of the larger of the two sides.

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