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Problem 17 Medium Difficulty

Critical Thinking $A B C$ is an isosceles triangle with base $\overline{B C} . X Y Z$ is an isosceles triangle with base $\overline{Y Z}$. Given that $\overline{A B} \cong \overline{X Y}$ and $\mathrm{m} \angle A=\mathrm{m} \angle X,$ compare $B C$ and $Y Z .$

Answer

$$B C=Y Z$$

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Video Transcript

you are asked to compare the length of side BC to the length of side Y Z well in our left triangle. It has described his Triangle, ABC as and I Saw Seles Triangle with base BC. The right triangle triangle X Y Z is also described as an I saw sleaze triangle Woodside y Z as its base. But you're also given the information that Syed A B is Congrats decide X y. So all of that information, um, has been marked. You're also told that the measurement of angle A is equal to the measurement of angle X. So with those items marked in the diagram, let's take the rest of the information and see what else we can mark the diagram by definition of I saw Seles A B and A C have to be the I sauce lease legs if side BC is the base of the triangle, so a C is congruent to a B and triangle. X Y Z xz must be congruent to X y again. They are the legs of the ice Aussies triangle. If y z is its base so we could see now Segment A C is congruent to segment X Z and we have the hinge here, um, applied here that says, If we know corresponding sides are congruent into triangles and we know the measurements of the included angle, then we know something about the sides opposite of those included angles well hinged, Arum says, if one angle is larger than the other than the side opposite of the larger angle is also a longer side than the side opposite of the smaller angle. In this case, our angles are congruent. Therefore, the signs opposite Ficken ruin angles have to be congruent sides. So if I had to compare the length of Segment BC to the length of segment Y Z, I would have to say their lengths are equal.

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