How to find if of acute / obtuse isosceles triangles are congruent

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ACT Math › How to find if of acute / obtuse isosceles triangles are congruent

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There are two obtuse triangles. The obtuse angle of triangle one is $101^{\circ}$ . The sum of two angles in the second triangle is $80^{\circ}$ . When are these two triangles congruent?

The two triangles cannot be congruent

The two triangles must be congruent

When the sum of angle A and angle B in triangle 1 is equal to the sum of the corresponding angles in triangle 2

When the obtuse angle is congruent to the smallest angle of the other triangle

Cannot be determined

Explanation

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 $101^{\circ}$ . That means the sum of the other two angles is $79^{\circ}$ . The sum of the corresponding angles in triangle 2 is $80^{\circ}$ . Therefore, because $79^{\circ}$ is not equal to $80^{\circ}$ , the two obtuse triangles cannot be congruent.

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