How to check 2 triangles are similar ?

Question

How to check 2 triangles are similar ?

Qustion 1:
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suppose, you have been given 2 triangle , triangle ABC and triangle DEF.

How do i check that 2 triangles are similar ?

shoul i check corresponding angles ...whther they are same or not ? again the "corresponding" is a vauge word...because if i rotate a triangle, then the meaning of "corresponding" changes .

whats the proper way to check 2 triangles are similar ?

Question 2:
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suppose, there are 2 triangles ABC and DEF....ok.....now you you found that they are similar by some deterministic way ......now, say, you rotate the second triangle a little.

can we say again , that ABC and DEF are still similar ? YES/NO ?
and why ?

Answer 1

"Two triangles are similar if their triples of vertex angles are the same."

1) therefore, you need to check that the angles are the same, and in the same order (example : triangle with angles 10,90,80 in the clockwise direction is similar to a triangle with 10.90.80 in clockwise direction, or 90,80,10 in clockwise direction... etc) either directly (measure them) or indirectly with a bit of trigonometry.

2) still similar. rotation doesn't afect the similarity. a positive homotetic transformation doesn't affect it either (getting it bigger or smaller). And neither does translation.


the source I give you is a good one for all kinds of maths problems. Please feel free to browse through it.

Answer 2

The answer to Question 2 is yes, just because you rotated it doesn't change anything.

The answer to Question 1 is a little more complicated. Probably best I just link the wikipedia article than try to explain it and mess it up. http://en.wikipedia.org/wiki/Similar_triangles

Short answer is this; If the 2 of the angles are the same than the triangles are similiar. If 2 of the sides are the same or proportionant than the triangles are similar. If they are the same than the triagles are congruent.

Corresponding means the equivalent. If your dealing with two right triangles, you could say the two right angles are corresponding angles.

Answer 3

a triangle has three lines. so it has three corners. there is some internal angle at the three corners...or vertices..

two triangles are similar if the internal angles in one triangles is same as the internal angles in the other triangle..

if you rotate the triangle then the internal angles dont change... so the triangles will still be similar...

i think you are confused about the corresponding angles..

if suppose and a in first triangle is equal to angle d in second then angle a is corresponding to angle c...

they will be corresponding if they are equal and if they are unequal then your triangle might not be similar... or you might have measured the non corresponding angles...

answer1
The meaning of corresponding angles dont change...however you measure. they will be corresponding only if they are equal... otherwise they will not be corresponding.
remember if your corresponding angles are equal then they are similar...

answer2
same as answer 1

Answer 4

Check the angles. If the corresponding angles are the same the triangles are similar.

Answer 5

u can use corresponding angles. to find corresponding angles then just measure the angles and find the same sizes. you can also do the same thing by measuring the sides. or you could go all complicated and start squaring the angles, or using tangent and cotangent but im guessing ur doing freshman geometry so you dont have to worry about those yet

Answer 6

to check whther two triangles are similar -

u must see that the corresponding angles of the two triangles are equal and their sides are proportional

Answer 7

answr1
dere r 3 ways of chkin whther or nt its similar or nt
1st:SSS rule(sides should b proportional)
i.e.ab/de=bc/ef=ac/df
2nd:AA rule(angles should be equal)
i.e. if any 2 anles r equal den dey r said 2 b similar
3rd:SAS rule(2sides proportional wid included angle equal)
i.e.ab/de=bc/ef,and angl B=angl E
now ur que is if it gets rotatd den wat?
d similarity is ritten in order i.e. if u say tri ABCis similar 2 tri DEF, den anglA shud b equal 2 anglD n B=E n C=F.den only abc is similar 2 DEFif nt its order changes
like ABC similar 2 DFE if A=D,b=f &C=E,evn if u rotate u will b knowin d angles.........rite????
answr2
yes it ll b similar
as rotatin wont change any angl nor changes any side's lenghth
just visuallization wud help u up

Answer 8

ana said it all = =
basically if any 2 angles of the two triangles are equal the = similar
if al 3 sides are proportional = similar.
if one looks like an enlarged proportion of another = similar.
if the textbook says it's similar.....then have no doubt.... it's similar = =

Answer 9

if d correspondin angles r eql or if d correspondin sides r proportional then d triangles r similar

Answer 10

u juz need to check the angle.... if the angles are samethey are similar