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Why does the SSA postulate work only with the right triangle?
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!
What is SSA in geometry?
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.
Is HL a special case of SSA?
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!
Is there an SAS postulate for similarity of two triangles also just as you have one for congruency of triangles?
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
When are two triangles said to be congruent?
Congruent means the same size and shape. Two triangles are congruent if the 3 sides and 3 angles of one are equal to the respective sides and angles, in order, of the other. Thus the triangles ABC and DEF are congruent if the lengths of AB and DE are equal, as well as BC and EF, and CA and FD, and the angle at A equals the angle at D, likewise that at B and at E, and of course if those two are true, the angle at C must equal the one at F since the 3 angles in a triangle always add up to 180 degrees. Two triangles are congruent if you can rigidly move one to exactly coincide with the other. It might be necessary to rotate it through 3-dimensional space, if the triangles are mirror images of each other. There are some theorems that give criteria that guarantee triangles to be congruent. One is side-side-side, abbreviated SSS, meaning that if the sides of two triangles, in order, are equal, so are the angles. Another is SAS, meaning two sides of one triangle and the angle included between them are equal to the corresponding parts of the other. If 2 of the angles of two triangles are the same (AA), so is the third, and the triangles are similar (same shape, but not necessarily the same size). Then all you need is that one side and the corresponding side in the other triangle are equal to prove congruence. There is one ambiguous case: SSA. Depending on the length of the side opposite the given angle, there may be 0, 1, or 2 different (non-congruent) triangles having the given part measures: 0 if the side is too short, 1 if it is the length of the perpendicular to the other side, and 2 if it is longer than that. Answer 1 ======= When they both have the same 3 interior angles and the same length of sides
