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

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find If Of Acute / Obtuse Isosceles Triangles Are Congruent

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?

Possible Answers:

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

Cannot be determined

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

The two triangles must be congruent

The two triangles cannot be congruent

Correct answer:

The two triangles cannot be congruent

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 . 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.

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