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November 13th, 2015, 04:56 AM   #1
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Are angles in similar triangle in the same proportion as the sides?

Are angles in similar triangle in the same proportion as the sides?

What I mean is, if I consider triangles ABC and DEF, where
AB:DE=1:2 then is angle C:angle F also 1:2?

Last edited by skipjack; November 13th, 2015 at 04:59 AM.
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November 13th, 2015, 05:00 AM   #2
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In general, no. As the triangles are similar, angles C and F are equal.
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November 13th, 2015, 07:10 AM   #3
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The crucial point is that, unlike the sides, the three angles in a triangle must add to 180 degrees. While the sides of one triangle might be 1/2 the sides of the other, the angles cannot be 1/2 the angles of the other since, then, they wouldn't add to 180 degrees.
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November 13th, 2015, 02:37 PM   #4
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Ok....so think of it this way... you know what zoom is right? Two similar triangles are made by zooming one so they have the same angles but the sides magnify/diminish by the same ratio, say all the sides are now .5 times the original ones or twice as large. Answer to your question is no btw since angles are in ratio 1:1 and sides are in a ratio that has nothing to do with the angles.

Last edited by skipjack; November 13th, 2015 at 11:51 PM.
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November 13th, 2015, 04:58 PM   #5
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Wait, my question was different. They are similar triangles so corresponding angles will be equal. I'm gonna edit my question. I actually combined two questions from my notebook.

Can't I edit my question?

Last edited by skipjack; November 13th, 2015 at 11:47 PM.
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November 13th, 2015, 05:17 PM   #6
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I made some mistake in identifying my queation. lol
I meant something else. How can I edit my question?

Last edited by skipjack; November 13th, 2015 at 11:48 PM.
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November 13th, 2015, 08:29 PM   #7
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November 14th, 2015, 07:23 PM   #8
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Not necessarily. If they are then they must be called as congruent triangle. Similar means similarity in shape and not in size, so similar means angles are similar and not the length of sides. A congruent triangle is similar but similar may not be congruent.
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