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There are 4 tests that can be used, depending upon what you have:
1) SSS (Side-Side-Side) - all three corresponding sides of the triangles are equal.
2) AAS (Angle-Angle-Side) - two corresponding angles and one corresponding side are equal
3) SAS (Side-Angle-Side) - two corresponding sides and the *ENCLOSED* angle are the same
4) RHS (Right angle-Hypotenuse-Side) - The triangles are Right-angled with Hypotenuse and corresponding side equal
In test 2, if two angles are given then the third angle can be calculated, thus the order does not matter and ASA(Angle-Side-Angle) is equivalent and also proves congruency.
Note the importance in test 3 that the angle is enclosed between the corresponding sides. If it is not enclosed, the triangles may be congruent, but they may also NOT be congruent. In this case the test you are using is Angle-Side-Side (ASS - which is what you would be to say that the triangles are congruent).
Note that RHS is a special case of ASS (the only one which guarantees congruency) in that the angle MUST be a right angle (90°); this means that the third side of both triangles can be calculated using Pythagoras and RHS is effectively SSS.
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If any two sides and any angle are congruent in two triangles then the triangles must be congruent?
False
If two triangles have three pairs of congruent angles then are the triangles guaranteed to be congruent?
false
If two triangles have three pairs of congruent angles then the triangles are not guaranteed to be congruent?
Correct. Congruency means that two triangles have three pairs of congruent angles and corresponding sides of the same lengths. A pair of triangles with three pairs of congruent angles but sides of different lengths are similar, not congruent.
Are two triangles with corresponding congruent angles congruent?
No, they are similar. They may be congruent, but they need not be.
Two triangles that have the same angles?
The triangles are similar, but not necessarily congruent.
What postulate or theorem verifies the congruence of triangles?
sssThere are five methods for proving the congruence of triangles. In SSS, you prove that all three sides of two triangles are congruent to each other. In SAS, if two sides of the triangles and the angle between them are congruent, then the triangles are congruent. In ASA, if two angles of the triangles and the side between them are congruent, then the triangles are congruent. In AAS, if two angles and one of the non-included sides of two triangles are congruent, then the triangles are congruent. In HL, which only applies to right triangles, if the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent.
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.
What does CPCTC mean in math terms?
CPCTC is an acronym for the phrase 'corresponding parts of congruent triangles are congruent' It means that once we know that two triangles are congruent, we know that all corresponding sides and angles are congruent.
In two triangles have a congruent angle and two congruent angle and two congruent sides then the triangles are guaranteed to be congruent?
Yes, if two triangles have two congruent angles and two congruent sides then the triangles are guaranteed to be congruent. They only need two angles and one side congruent or two sides and one angle in order to be congruent.
If two triangles have a congruent angle and two congruent sides then are the triangles guaranteed to be congruent?
Only if the congruent angle is the angle between the two congruent sides (SAS postulate).
The term for two triangles that are congruent after a dilation is?
The term for two triangles that are congruent after a dilation is similar.
Is it true that two triangles have 3 pairs of congruent angles then the triangle are not guaranteed to be congruent?
When two triangles are congruent, there are 6 facts that are true about the triangles. The triangles have 3 sets of congruent (of equal length) sides and the triangles have 3 sets of congruent (of equal measure) angles.
When working with congruent triangles why is it only necessary to be given two pairs of congruent angles to know that all three pairs of angles will be congruent?
Because ALL triangles total 180o...
Are two triangles are congruent if they have the same base?
No. All corresponding sides and angles have to be congruent for the triangles to be congruent.
If all corresponding sides and angles of two triangles are congruent those triangles are?
The triangles are also congruent.
What is c.p.c.t?
Corresponding Parts of Congruent Triangles is the full form od CPCT.
If any two sides and any angle are congruent in two triangles then the triangles must be congruent?
False
