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Problem 29 Hard Difficulty

Write About It Compare the Hinge Theorem to the SAS Congruence Postulate. How are they alike? How are they different?

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Video Transcript

Let's take a look at the difference between side angle side congruence there, Um, and the hinge here, what is the same between these two theorems is they both require two sides and an angle included between the two sides in the side angle side there, um, it says take two triangles and you've got two sides of that. You know their length and they are corresponding and congratulate in the two triangles. So in this diagram, E corresponds to B E and they are congruent. Side ce corresponds decide d e and their congruent. And we know the included angle in between the concurrent sides and our angle included between the crew current science is also can grow up. So if I was to change the shape of the triangles as long as the two theorems hold true and that is we've got corresponding congrats sides and the angle between the corresponding congruent sides is also congruent or two angles or two triangles are congruent. It doesn't matter if I change the length of the sides or the angle between them side angle side congregants, their states that two sides corresponding in Groot and an included angle congruent makes the two triangles can groped. However, in a side angle side hinge There, um, we start out with two triangles that appear to fit the side angle Side can grew its there. But as soon as we change the length of one side of a triangle, we still have A is corresponding to B E and is congruent We've got CE is corresponding to d e and there congruent but the included angle Zehr no longer can grouped hinge there. Um, States, if we have the correspondent congruent sides and the included angle if we know the measurement of the angle, we know something about the third side of the triangles and in this case, in triangle B E. C. The included angle is 77.2, which is larger than angle a D at 52. And if you'll notice a soon as I made the angle larger or third side of our triangle became longer than the third side of this triangle. Here I can continue to make those inferences again are corresponding. Concurrent sides remain the same, but if I change the included angle, the larger of the two included angles will be opposite of a longer segment, the smaller of the two included angles will be opposite of a smaller segment or shorter segment. This holds true for the hinge here, um

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