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If two triangles are similar, does that mean they are congruent too?

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danigrlc | Student | eNotes Newbie

Posted September 18, 2010 at 9:05 AM via web

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If two triangles are similar, does that mean they are congruent too?

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pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted September 18, 2010 at 9:43 AM (Answer #1)

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When triangles are similar, they could be congruent.  However, they do not have to be congruent in order to be similar.  So I guess the answer is not always.

When triangles are similar, their angles are the same.  But that does not mean that they have to be congruent.  They can have the same angles but have sides of different lengths.  So you can have two triangles where the angles are the same but where one has sides that are all 3 times the length of the other, for example.  In such a case, the two triangles would be similar but not congruent.

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neela | High School Teacher | (Level 3) Valedictorian

Posted September 18, 2010 at 2:41 PM (Answer #2)

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  Two triangles are similar  and two triangles are congruent do not mean the same thing.

Two photos of the same object may look similar though their sizes are different.

Two photos of the same object are congruent if their sizees are same .

If two triables are similar if their for each angle of the one there is an equal angle in the other triangle. This reltion holds incase of cogruency also.

If two triangles are similar, then the correspoding sides (corresponding side implies side opposite to the equal angles in two triangles)  has the same ratio.

Or if ABC and A'B'C' are two similar triangles, then  angles, A=A', B = B' and C = C' .The ratio of corresponding sides, AB/A'B' = BC/B'C' = CA/C'A'.

If  the two triangles are congruent AB/B'C' = BC/B'C' = CA/C'A' = 1. In other words, AB = A'B' , BC = B'C' and CA = C'A'.But in case of sim'lar triangles , this side equality ratio is not necessary.

All congruent triangles are similar. Allsimilar triangles are not congruent.

Congruent triangles are a special subset class of triangle.

 

 

 

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william1941 | College Teacher | (Level 3) Valedictorian

Posted September 18, 2010 at 4:18 PM (Answer #3)

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Congruent triangles have equal angles as well sides with equal lengths. The triangles are the same in every respect.

Similar triangles on the other hand are either congruent or the lengths of their sides have the same ratio. That is, one triangle can have sides of length 3, 4 and 5 cm and the other can have sides of length 6, 8 and 10 cm respectively. If the ratio of the lengths of their sides is equal to one, they are congruent.

So all congruent triangles have to be similar but all similar triangles need not be congruent.

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atyourservice | Student, Grade 10 | (Level 3) Valedictorian

Posted May 26, 2014 at 3:32 PM (Answer #4)

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No, if two triangles are similar, it doesnt mean they are congruent too. There is a chance they are congruent but similar means they have things in common such as their angle measurement and such, while congruent means equal in every aspect.

 

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