Geometry Proof Perpendicular Lines
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Uploader Comments (drenniemath)
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Lots is wrong here.
1. The Hinge Theorem can't be used to show that angles ABD and ADB are congruent. Hinge Theorem allows for comparison of triangles in which two sides are congruent to two sides and the included angles are not congruent.
2. The Base Angles Theorem can't be used to do it either. Base Angles Theorem assumes that angles are congruent and concludes that sides are congruent. We need to do precisely the opposite.
3. Use SSS to begin, not SAS. It's easier. Lots
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1) While the Hinge Thm does work when making comparisons between two triangles, the other consequence of it is that given congruent angles within a single triangle the triangle must be congruent. This falls out of the other related topics of "within a single triangle smaller angles are opposite smaller sides.
2) The Base Angle Thm and its converse both hold true; thus you are arguing a semantic point.
3) I can see the SSS on the larger triangles now that you point that out.
drenniemath 8 months ago