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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 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
What are the ways you can show that triangles are similar?
You can use the theorems like SSS, SSA to show that they are similar. For example if two triangles have the same 3 sides length or two side lengths equal and 1 angle equal they are similar. * * * * * That is congruent, not similar! Similar is a weaker requirement. All that is needed is that two corresponding angles are the same. Equivalently, the three corresponding sides are in the same proportion.
Is ssa a conguent theorem or postulate?
No. SSA can give rise to a pair of non-congruent triangles.
What are three ways that you can prove that triangles are congruent?
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.
Which arrangement cannot be used to prove two triangles congruent?
SSA
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 ass or ssa congruence postulate?
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.
Ssa sas sss which of these mean congruent?
SAS and SSS are congruent. SSA need not be.
AAA angle angle angle guarantees congruence between two triangles?
true apex :)
SSA does not guarantee congruence between two triangles?
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.
Why is SSA not a congruent shortcut?
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.
SSA side-side-angle guarantees congruence between two triangles?
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).
If one pair of opposite angles and one pair of opposite sites of a quadrilateral is congruent then the quadrilateral is a parallelogram. How can it be proven?
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.
Does SSA guarantees congruence between two triangles?
false
