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

Study concepts, example questions & explanations for ACT Math

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Example Questions

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

Observe the following image and answer the question below:


Are triangles  and  congruent?

Possible Answers:

Not enough information to decide.




Correct answer:



Two triangles are only congruent if all of their sides are the same length, and all of the corresponding angles are of the same degree. Luckily, we only need three of these six numbers to completely determine the others, as long as we have at least one angle and one side, and any other combination of the other numbers.

In this case, we have two adjacent angles and one side, directly across from one of our angles in both triangles. This can be called the AAS case. We can see from our picture that all of our angles match, and the two sides match as well. They're all in the same position relative to each other on the triangle, so that is enough information to say that the two triangles are congruent.

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