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# Make a conclusion based on the Hinge Theorem or its converse. (Hint: Draw a sketch.)In $\triangle A B C$ and $\triangle D E F, \overline{A B} \cong \overline{D E}, \overline{B C} \cong \overline{E F}, \mathrm{m} \angle B=59^{\circ},$ and $\mathrm{m} \angle E=47^{\circ}$

## $m \angle P S R<m \angle P Q R$

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Let's see what we conclude based on some given information. We want to draw Triangle ABC and we want to try to draw a triangle D E f. We want to know. Take that segment. A B is congruent to segment d E. They are corresponding segment BC is congruent to segment e o f. They are corresponding and the measurement of angle B is 59 degrees. That is thean included angle of a triangle, ABC and we also know the measurement of angle is 47 degrees. This information sets up using the hinge here, um, which states of two sides or corresponding and congruent of two triangles, but the included angles are not congruent. Then we know something about the sides opposite of the angles. The side opposite of the larger angle is longer than the side opposite of the smaller angle, so we can conclude the length of Segment A C is greater than the length of segment D. F

University of Oklahoma

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