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What must be shown to be congruent in order to say that the triangles are congruent by SAS?
Two sides and the included angle of one triangle must be congruent to two sides and the included angle of the other.
If any two sides and any angle are congruent in two triangles then the triangles must be congruent.?
No. The angles must be an included angle, between the sides to guarantee congruence. For an example. imagine a triangle with two equal sides and a 60 degree angle between them and another triangle with the same two equal sides and a 120 degree angle between them.
What else must you know to prove the triangles congruent by SAS?
Nothing. If a side ,an angle, and a side are the same the triangles are congruent.
What is the sss rule?
if you have two triangles you can prove them congruent by stating that all of the sides are congruent, hence (SSS=Side, Side, Side). You can also do the same by stating SAS (Side, Angle, Side) or ASA (Angle, Side, Angle). Using these methods, everything must be in order and consecutive to prove the triangles congruent good question
Can any two triangles be joined to make a rhombus?
No. A rhombus has all four sides of equal length. To split a rhombus into only 2 triangles, it must be split along a diagonal; which means that 2 of the sides of one of the triangles must be the same length as the sides of the rhombus, which being equal mean the triangles must be (at least) isosceles - scalene triangles will not work. Further, as the diagonal will be a common length to each of the triangles (the length of their third sides), it will form the base (ie the side opposite the vertex between the sides of equal length) of the isosceles triangles, and so the triangles must be to congruent isosceles triangles. If the diagonal has the same length as the side of the rhombus, then the two congruent triangles will be congruent equilateral triangles.
What must be shown to be congruent in order to say that the triangles are congruent by SAS?
Two sides and the included angle of one triangle must be congruent to two sides and the included angle of the other.
If any two sides and any angle are congruent in two triangles then the triangles must be congruent.?
No. The angles must be an included angle, between the sides to guarantee congruence. For an example. imagine a triangle with two equal sides and a 60 degree angle between them and another triangle with the same two equal sides and a 120 degree angle between them.
If two triangles have three pairs of congruent angles the the triangles are not guarenteed to be congruent?
If two triangles have three pairs of congruent angles, they are said to be similar but not necessarily congruent. Similar triangles have the same shape but can differ in size, meaning their corresponding sides are in proportion but not equal. For triangles to be congruent, both their angles and corresponding sides must be equal, which is not guaranteed if only angle congruence is established. Therefore, while angle congruence indicates similarity, it does not ensure congruence.
Similar triangles must have congruent angles and congruent sides?
False dood
What else must you know to prove the triangles congruent by SAS?
Nothing. If a side ,an angle, and a side are the same the triangles are congruent.
What is the sss rule?
if you have two triangles you can prove them congruent by stating that all of the sides are congruent, hence (SSS=Side, Side, Side). You can also do the same by stating SAS (Side, Angle, Side) or ASA (Angle, Side, Angle). Using these methods, everything must be in order and consecutive to prove the triangles congruent good question
If two triangles have equivalent angle measures then they are congruent?
If two triangles have equivalent angle measures, they are similar, but not necessarily congruent. Similar triangles have the same shape but can differ in size, meaning their corresponding sides are proportional, but not necessarily equal. Congruent triangles must have both equal angles and equal side lengths. Therefore, while equivalent angles imply similarity, they do not guarantee congruence.
Postulate or theorem used to prove two triangles are congruent?
You can use a variety of postulates or theorems, among others: SSS (Side-Side-Side) ASA (Angle-Side-Angle - any two corresponding sides* and a corresponding angle) SAS (Side-Angle-Side - the angle MUST be between the two sides, except:) RHS (Right angle-Hypotenuse-Side - this is only ASS which works) * if two corresponding angles are the same, then the third corresponding angle must also be the same (as the angles of a triangle always sum to 180°), and that can be substituted for one angle of ASA to get AAS or SAA.
What is congruent angle?
Congruent angles are of the same size as for example 85 degrees is congruent to 85 degrees
Can any two triangles be joined to make a rhombus?
No. A rhombus has all four sides of equal length. To split a rhombus into only 2 triangles, it must be split along a diagonal; which means that 2 of the sides of one of the triangles must be the same length as the sides of the rhombus, which being equal mean the triangles must be (at least) isosceles - scalene triangles will not work. Further, as the diagonal will be a common length to each of the triangles (the length of their third sides), it will form the base (ie the side opposite the vertex between the sides of equal length) of the isosceles triangles, and so the triangles must be to congruent isosceles triangles. If the diagonal has the same length as the side of the rhombus, then the two congruent triangles will be congruent equilateral triangles.
Can any triangles be joined to make a rhombus?
No. A rhombus has all four sides of equal length. To split a rhombus into only 2 triangles, it must be split along a diagonal; which means that 2 of the sides of one of the triangles must be the same length as the sides of the rhombus, which being equal mean the triangles must be (at least) isosceles - scalene triangles will not work. Further, as the diagonal will be a common length to each of the triangles (the length of their third sides), it will form the base (ie the side opposite the vertex between the sides of equal length) of the isosceles triangles, and so the triangles must be to congruent isosceles triangles. If the diagonal has the same length as the side of the rhombus, then the two congruent triangles will be congruent equilateral triangles.
To use the HL Theorem to prove two triangles are congruent the triangles must be right triangles. Which other conditions must also be met?
The two legs must be corresponding sides.
