The triangle ABC is a right triangle.
Which angle is larger, or ?
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The triangle ABC is a right triangle.
Which angle is larger, or ?
In a right triangle , angle is the right angle, which equals 90°. Therefore, the other two angles and must sum to 90°.
For any right triangle, if one acute angle is larger, the opposite side (leg) is longer. Conversely, if an angle is smaller, the opposing leg must be shorter.
Based on the triangle's diagram and fundamental right triangle properties, it appears that angle is larger than angle , given that larger angles oppose longer sides.
This conclusion follows from practical geometry, where angle recognition and placement determine relative size.
Therefore, we can conclude that is greater than , or .
Is DE side in one of the triangles?
Look at the sides opposite each angle! In triangle ABC, angle A is opposite side BC, and angle B is opposite side AC. The longer side means the larger angle.
They could be equal, but only in a special case called a 45-45-90 triangle where the two legs are equal length. In most right triangles, the legs have different lengths.
This is a fundamental rule: larger angles are always opposite longer sides, and smaller angles are opposite shorter sides. This works in any triangle!
The side opposite an angle is the side that doesn't touch that angle's vertex. For example, side BC is opposite angle A because it connects points B and C, not point A.
The diagram is crucial here! It shows the relative positions and lengths of the sides. Without visual information, you'd need actual measurements or additional given information.
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