Are Proportional Sides Enough to Prove Equal Angles in Similar Triangles?

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Proportional sides in triangles indicate that the triangles are similar, which means their corresponding angles are equal. In the context of a parallelogram, proving that segments BX and DY are parallel involves demonstrating that corresponding angles are equal. The discussion highlights the importance of understanding geometry concepts, especially before tests. The clarification about similar triangles reinforces the relationship between side proportions and angle equality. Overall, proportional sides are sufficient to prove equal angles in similar triangles.
dekoi
Oddly enough, i forget my geometry laws two days before the test.

If ABCD is a parallelogram where x and y are on the midpoints of AD and BC. Prove that BX and DY are parallel. I understand one would have to prove that corresponding angles are equal. thus, AHX would equal CMY, and ADM would equal BHC.

My question is: if a large triangle and a smaller triangle have proportional sides (e.g. 1/2), would the angles be proven equal?
 
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Hey, you're not supposed to forget until AFTER the test!


Yes, if two triangles have sides in proportion, then they are "similar" triangles and have the same angles.
 
Thank you HallsofIvy for reminding me about the similar triangles, as well as to forget everything i know after the test. :)
 

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