# Why can't there be an axiom of congruency of triangles as A.S.S. similar to R.H.S.?

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I think that, if we consider 2 triangles, whose one angle, the side opposite to that angle and any other side are equal, then the two triangles are congruent. If I am wrong, can someone please construct 2 non-congruent triangles with these conditions?

I think that, if we consider 2 triangles, whose one angle, the side opposite to that angle and any other side are equal, then the two triangles are congruent. If I am wrong, can someone please construct 2 non-congruent triangles with these conditions?

If #C# is the center of a circle, the #abs(CB)=abs(CD)#

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The A.S.S. (Angle-Side-Side) condition is not a valid criterion for triangle congruence because it can lead to ambiguity and does not uniquely determine a triangle. Unlike the R.H.S. (Right Angle-Hypotenuse-Side) condition, which is a valid criterion for congruence in right triangles, the A.S.S. condition may result in multiple triangles with different shapes and sizes that satisfy the given conditions.

Specifically, the A.S.S. condition does not account for the fact that given two angles and a side length, there may be more than one triangle that can be constructed. This ambiguity violates the requirement of a valid axiom, which should lead to a unique geometric outcome.

Therefore, the A.S.S. condition cannot be used as an axiom of congruency for triangles because it does not provide sufficient information to uniquely determine congruent triangles.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Triangle A has an area of #5 # and two sides of lengths #9 # and #3 #. Triangle B is similar to triangle A and has a side with a length of #9 #. What are the maximum and minimum possible areas of triangle B?
- A triangle has corners points A, B, and C. Side AB has a length of #15 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #18 #, what is the length of side BC?
- A triangle has corners at points A, B, and C. Side AB has a length of #48 #. The distance between the intersection of point A's angle bisector with side BC and point B is #24 #. If side AC has a length of #32 #, what is the length of side BC?
- Triangle A has sides of lengths #48 ,24 #, and #27 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the possible lengths of the other two sides of triangle B?
- Triangle A has an area of #84 # and two sides of lengths #18 # and #15 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the maximum and minimum possible areas of triangle B?

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