Which of the triangles are congruent?
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Which of the triangles are congruent?
Let's observe the angle in each of the triangles and note that each time it is opposite to the length of a different side.
Therefore, none of the triangles are congruent since it is impossible to know from the data.
It is not possible to know based on the data.
Look at the triangles in the diagram.
Which of the statements is true?
Having the same angle measure doesn't guarantee congruence! The 45° angle might be opposite different sides in each triangle. For congruence, we need corresponding parts to be equal - angles and sides in the same relative positions.
You'd need to know which sides the 45° angles are opposite, plus additional matching sides or angles. For example: SAS (two sides and included angle), ASA (two angles and included side), or SSS (all three sides).
Check if you can apply any congruence theorem (SAS, ASA, AAS, SSS, or HL). If you can't match the required corresponding parts, then the information is insufficient to prove congruence.
Possibly, but in mathematics we can only conclude what we can prove. Without sufficient given information, the answer is always 'impossible to determine' rather than making assumptions.
Corresponding parts are sides and angles in the same relative position. For example, if angle A in triangle 1 is the largest angle, it corresponds to the largest angle in triangle 2, not just any 45° angle.
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