How to find if of acute / obtuse isosceles triangles are congruent - ACT Math
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Question
There are two obtuse triangles. The obtuse angle of triangle one is 
. The sum of two angles in the second triangle is 
. When are these two triangles congruent?
There are two obtuse triangles. The obtuse angle of triangle one is
Answer
In order for two obtuse triangles to be congruent, the sum of the two smaller angles must equal the sum of the two smaller angles of the second triangle. That is, excluding the obtuse angle.
The first triangle has an obtuse angle of 
. That means the sum of the other two angles is 
. The sum of the corresponding angles in triangle 2 is 
. Therefore, because 
is not equal to 
, the two obtuse triangles cannot be congruent.
In order for two obtuse triangles to be congruent, the sum of the two smaller angles must equal the sum of the two smaller angles of the second triangle. That is, excluding the obtuse angle.
The first triangle has an obtuse angle of
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