SOLUTION: Sara says: I have drawn a triangle. It has one angle of 60o and one side 2 inches long. Sanjay, you draw a triangle with the same two properties. Sanjay says: My triangle will b

Algebra ->  Triangles -> SOLUTION: Sara says: I have drawn a triangle. It has one angle of 60o and one side 2 inches long. Sanjay, you draw a triangle with the same two properties. Sanjay says: My triangle will b      Log On


   

Question 1131873: Sara says: I have drawn a triangle.
It has one angle of 60o and one side 2 inches long.
Sanjay, you draw a triangle with the same two properties.
Sanjay says: My triangle will be congruent to yours, because all triangles that have those two properties must be congruent.
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Triangles are congruent if:
SSS (side side side)
All three corresponding sides are equal in length.
SAS (side angle side)
A pair of corresponding sides and the included angle are equal.
ASA (angle side angle)
A pair of corresponding angles and the included side are equal.
AAS (angle angle side)
A pair of corresponding angles and a non-included side are equal.
HL (hypotenuse leg of a right triangle)
Two right triangles are congruent if the hypotenuse and one leg are equal.

If you and Sanjay have drawn a triangle that has one angle of 60° and one side 2 inches long, there is no sufficient data to prove two triangles are congruent.



Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Sanjay is wrong.  The triangles are not necessarily congruent.  
Just the two properties, a side and an angle, are not enough,
Both triangles below have a 60° angle and a side which is
2 inches long, but they are not the same shape and therefore not
congruent:




Edwin