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

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SUMMARY

In the discussion, it is established that if two triangles have proportional sides, they are classified as similar triangles, which guarantees that their corresponding angles are equal. The example provided illustrates a scenario involving a parallelogram ABCD with midpoints x and y on sides AD and BC, respectively, and emphasizes the need to prove that BX and DY are parallel by demonstrating the equality of corresponding angles. The conclusion reinforces the fundamental property of similar triangles in geometry.

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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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