No. SSA is ambiguous. Unless A = 90 degrees, there are two possible configurations for the triangle. So they need not be congruent.
You can't use SSA or ASS as a postulate because it doesn't determine that the triangles are congruent; right triangles are most likely determined by HL: hypotenuse leg- genius!
SSA (Side-Side-Angle) cannot be a proof of triangle congruence because it does not guarantee that the two triangles formed are congruent. The angle can be positioned in such a way that two different triangles can have the same two sides and the same angle, leading to the ambiguous case known as the "SSA ambiguity." This means two distinct triangles could satisfy the SSA condition, thus failing to prove congruence. Therefore, other criteria like SSS, SAS, or ASA must be used for triangle congruence.
It refers to the congruence of two sides and a non-included angle of one triangle with that of another. SSA does not imply congruence of the triangles.
Oh, what a lovely question! HL, which stands for Hypotenuse-Leg, is indeed a special case of the Side-Side-Angle postulate in geometry. When we have two triangles where we know the length of one side, the length of another side, and the measure of an angle not between those sides, we can use the SSA postulate to determine if the triangles are congruent. Keep exploring the beauty of geometry, my friend!
YesFor 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
No. SSA can give rise to a pair of non-congruent triangles.
SSA
If triangles have the corresponding sides congruent then they are congruent. SSS If two triangles have two sides and an included angle congruent then they are congruent. SAS If two triangles have two angles and an included side congruent then they are congruent. ASA SSA doesn't work.
You can't use SSA or ASS as a postulate because it doesn't determine that the triangles are congruent; right triangles are most likely determined by HL: hypotenuse leg- genius!
The ASS postulate would be that:if an angle and two sides of one triangle are congruent to the corresponding angle and two sides of a second triangle, then the two triangles are congruent.The SSA postulate would be similar.Neither is true.
SAS and SSS are congruent. SSA need not be.
true apex :)
True. Only if the given angle is between the two sides will the two triangles guarantee to be congruent (SAS), unless the given angle is a right angle (90°) in which case you now have RHS (Right-angle, Hypotenuse, Side) which does guarantee congruence.
SSA is ambiguous. If A is not a right angle, then there are two possible configurations for the triangle. So they need not be congruent.
trueTrue -- SSA does NOT guarantee congruence.Only SAS, SSS, and ASA can do that (and AAS, because if two pairs of corresponding angles are congruent, the third has to be).
draw a diagonal through opposite corners of the quadrilateral. This makes two triangles. Prove the triangles are congruent using SSA (side side angle) congruence. Then show that the other two sides of the quadrilater must be congruent to each other, so it is a parallelogram.
false