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# Is there an SAS postulate for similarity of two triangles also just as you have one for congruency of triangles?

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###### 2015-09-24 22:08:48
Yes

For two triangles to be congruent, their corresponding sides must be of equal length. But for triangles to be similar, they must only have equal angles. For there to be a SAS postulate for similarity, the two corresponding sides would have to be proportionate, not equal. If they were equal, the triangles would be congruent.

So, an SAS postulate for similar triangles would mean that two of the sides of the smaller triangle are, for example, half the two corresponding sides of the other triangle. If also the corresponding included angles are equal, then the two triangles would be similar triangles.

APEX: similar
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###### 2014-06-24 22:41:41

No. SSA is ambiguous.

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## Related Questions

SSS is a postulate used in proving that two triangles are congruent. It is also known as the "Side-Side-Side" Triangle Congruence Postulate. It states that if all 3 sides of a triangle are congruent to another triangles 3 sides, then both triangles are congruent.

From ancient times, properties of quadrilaterals have been used especially in art, design and architecture. Diagonal of a rectangle divides it into two congruent triangles and the idea of congruency especially in triangles had been used by Egyptians to build The Great Pyramids of Giza!!!!! The idea of congruency of triangles initially from diagonal of quadrilaterals also helped Leonardo Da Vinci to paint the world famous 'Monalisa'!!!!! So, what other wonders do you want from quadrilaterals????!!!????

Rules for congruency of triangles 1. Sss- three sides are equal 2. Sas- when two sides and one angle are equal 3. Aas- two angles and one side are equal. Rules for similarity of triangles 1.aa - two anles equal hence third also 2. Sss - ratio of corresponding sides is equal.

Postulate:- A statement that is accepted as true, that forms the basis of a theory, etc.It also has a synonym:- posit

In classical studies, it is also called a postulate.

No. All equilateral triangles are isosceles, but not all isosceles triangles are equilateral.

Yes. But not all isosceles triangles are equilateral.

euclidean Geometry where the parallel line postulate exists. and the is also eliptic geometry where the parallel line postulate does not exist.

They are: right angle, isosceles and equilateral triangles There are also scalene and obtuse triangles

No because all right triangles have 2 legs and a hypotenuse. The hypotenuse is always longer than either leg so right triangles can't be equilateral triangles.

Two equilateral triangles can form a rhombus- it can also be formed by using a higher number of isosceles triangles.

This is Euclid's fifth postulate, also known as the Parallel Postulate. It is quite possible to construct consistent systems of geometry where this postulate is negated - either many parallel lines or none.

Scalene triangles those triangles in which all the sides are of different lengths, but in isosceles triangles two sides of the triangle are equal in length. Therefore, no scalene triangle can ever be isosceles.

There are 4 tests that can be used, depending upon what you have:1) SSS (Side-Side-Side) - all three corresponding sides of the triangles are equal.2) AAS (Angle-Angle-Side) - two corresponding angles and one corresponding side are equal3) SAS (Side-Angle-Side) - two corresponding sides and the *ENCLOSED* angle are the same4) RHS (Right angle-Hypotenuse-Side) - The triangles are Right-angled with Hypotenuse and corresponding side equalIn test 2, if two angles are given then the third angle can be calculated, thus the order does not matter and ASA(Angle-Side-Angle) is equivalent and also proves congruency.Note the importance in test 3 that the angle is enclosed between the corresponding sides. If it is not enclosed, the triangles may be congruent, but they may also NOT be congruent. In this case the test you are using is Angle-Side-Side (ASS - which is what you would be to say that the triangles are congruent).Note that RHS is a special case of ASS (the only one which guarantees congruency) in that the angle MUST be a right angle (90ยฐ); this means that the third side of both triangles can be calculated using Pythagoras and RHS is effectively SSS.

The simplest pattern is 2n+1, so the 16th figure will have 33 triangles. Of course, if you are creating new triangles and also keeping the old triangles, this would be different.

All equilateral triangles are acute triangles, since all the angles are less than 90 degrees.

... given line. This is one version of Euclid's fifth postulate, also known as the Parallel Postulate. It is quite possible to construct consistent systems of geometry where this postulate is negated - either many parallel lines or none.

Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other.When two triangles have corresponding sides with identical ratios, the triangles are similar.Of course if triangles are congruent, they are also similar.

Yes. Consider the situation when: the right-angled triangles are also isosceles and the hypotenuse (longest side) of the triangles is equal to the side of the square. If you surround a square with four of right-angled triangles (the sides of the square being in contact with the hypotenuses of the triangles), you get a larger shape which is also a square. Taking this as a basic unit, you can make a tesselations. You can also make tessalations if you have two sets of squares, one with sides the same length of the hypotenuse of the triangles and one with sides the same length as the smaller sides of the triangles.

Assuming ALL 22 triangles are congruent, this would be a 22-gon, also known as an icositedigon

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