# If 3 sides of one triangle are directly proportional to 3 sides of a second triangle then the triangles are similar?

SSS Similarity, SSS Similarity Theorem, SSS Similarity Postulate

### Mathematics similarities of triangles?

Two triangles are considered to be similar if for each angles in one triangle, there is a congruent angle in the other triangle. Two triangles ABC and A'B'C' are similar if the three angles of the first triangle are congruent to the corresponding three angles of the second triangle and the lengths of their corresponding sides are proportional as follows: AB / A'B' = BC / B'C' = CA / C'A'

### Can bisector of angle divide the triangle into similar triangle?

Given certain triangles, it would be possible for an angle to be bisected and create two new triangles which are similar to each other. And in the case of a [45Â°, 45Â°, 90Â°] right triangle, if you bisect the right angle, then you will create two new [45Â°, 45Â°, 90Â°] triangles (both similar to each other and similar to the original).

### Why are all equilateral triangles similar?

DFN: we call a triangle equilateral if all sides of the triangle are the same length DFN:we call two triangles similar if corresponding angles are equal, and corresponding sides are proportional. First show that all corresponding sides are proportional: Consider a equilateral triangle with side lengths 1, all other equal lateral triangles sides can be expressed as S*(1), where S is some scalar. Hence all equilateral triangles sides are proportional to each other. Next, show…

### Are all isosceles triangles are similar?

No. For a triangle to be isosceles, it must have 2 angles both equal to x, and one angle equal to y where 2x + y = 180o. For two triangles to be similar, they must have all 3 angles equal. An example of 2 triangles which are both isosceles, yet not similar are triangle ABC with angles 50o, 50o and 80o, and triangle DEF with angles 40o, 40o and 100o.

### Are congruent triangles always similar?

No, congruent triangles are always similar but similar triangles and not always congruent. Imagine that similar triangles can be created on a copy machine enlarge and shrink the image, turn it, even turn it over, the angles remain the same. A congruent triangle must be exactly the same as the original. Hope this helps!

### What is a three sided polygons with the same shape but not the same size are called?

Three sided polygons would be triangles. Triangles that have the same shape (same angle measures) but are different sizes (different side lengths) would be called similar triangles. In similar triangles, corresponding sides have lengths in the same ratio. If triangle ABC is similar to triangle DEF, then: AB/DE = BC/EF = AC/DF.

### Difference between similar triangles and congruent triangles?

Similar triangles are two triangles with three identical angles but not necessarily identical lengths but if they aren't identical they must have an identical scale factor for each side. Congruent triangle have identical angles and lengths but mat be rotated. on a similar triangle if one size gets bigger by two times the original all of them must be two times the original.

### When is an equiangular triangle not equilateral?

If a triangle is equiangular, it will have all equal angles. So, it might be similar to another equiangular triangle, but not congruent. It is not equilateral if the sides are not equal in length. All equiangular triangles are similar, but not all of them are congruent, which means they do not all have corresponding side lengths. But, all equilateral triangles are equiangular.