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Pweez sumone explainz!
two triangles are said to be similar if:Originally Posted by whytechocolate01
What postulate or theorem justifies the statement..Triangle ABC is similar to Triangle RST...
1) corresponding angles are equal
2) the ratio of corresponding sides are equal
the second posulate is what justifies the statement that these triangles are similar.
we see that side rs of one triangle corresponds to side ab of the other, and side st of one triangle corresponds to side bc of the other.
if these triangles are similar, then, for example:
rs/st = ab/bc
now, rs/st = 5/6
and ab/bc = 10/12 = 5/6 = rs/st
thus the triangles are similar
I don't really understand this question. From the given information we cannot say if these two triangles are similar or not because we have no information about the third side and don't know any of the angles.What postulate or theorem justifies the statement..Triangle ABC is similar to Triangle RST...
IF the ratio of the lengths of sides rt/ac = 5/10 = 6/12 or IF angles s and b are equal then we may say that the two triangles are similar.
-Dan
The first 2 sides are equal with an enlargement value of two.What postulate or theorem justifies the statement..Triangle ABC is similar to Triangle RST...
So the third side will also be equal.
To prove this theorem takes a little bit more...
We first have to construct a triangle the size of the little one inside the bigger one.
Then prove them congruent.
Then we must prove their angles equal, which is relatively easy.
If you want me to thoroughly explain it to you, just ask and i'll be happy to do it.
if we have two sides proportional, can we not assume that the third side is proportional as well
can you come up with a counter-example for such an assumption?I disagree. We may construct two triangles, one with angle s equal, say, to 30 degrees, and angle b equal to 25 degrees.
Then: rt = sqrt{5^2 + 6^2 + 2*5*6*cos(30)} = 10.6283
Then ac = sqrt{10^2 + 12^2 + 2*10*12*cos(25)} = 21.4829
and rt/ac = 0.494735
which is not the required 1/2.
-Dan
Two triangles are similar if they have the same angles, or if ALL of the sides are in the same proportions to each other. We don't have enough information from either triangle to state what any of the angles are, and we don't have enough information to calculate that third side, so we can't say they are similar.
This is almost a trick question. The diagrams that are given are drawn to show that the angles are the same, which is meant to throw you off. NEVER trust the way a sketch looks, depend only on the numbers.
-Dan
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