To determine whether the two triangles can be shown to be congruent using the Angle-Side-Angle (ASA) criterion, we need to understand the conditions for applying ASA.
ASA states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Here's how to analyze the options provided:
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Calculate the Missing Angle: If you can deduce that the missing angle in the pink triangle is 100 degrees using the triangle angle sum theorem (which states that the sum of the angles in a triangle is always 180 degrees), this information is necessary for establishing congruence.
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Count the Known Angles and Sides: You need to check whether there are indeed 2 angles and the included side available in both triangles.
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Evaluate the Options:
- The first option suggests calculating the missing angle in the pink triangle and then using ASA. If the conditions for ASA are satisfied (2 angles and included side), this option could be valid.
- The second option states that there are 2 angles and 1 side given in each triangle. If this is true and the side is included between the two known angles, then ASA can be applied.
- The third option states they cannot be shown to be congruent with ASA. This would only be true if the criteria for ASA are not satisfied.
Conclusion: Depending on the specifics of the triangles in question:
- If both triangles have 2 angles and the included side, then "Yes, because there are 2 angle measurements given in each triangle and 1 side" is the correct choice.
- If you can calculate the missing angle and confirm the structure allows for ASA, then "Yes, by using the triangle angle sum theorem" could be valid as well.
If the angles don't align or there isn't a side that fits the ASA requirement, then "No, they can not be shown congruent with ASA" would be the answer.
Given this information, the second response is the most straightforward if it accurately describes the situation with both triangles.
1 answer