To provide you with appropriate answers and solutions, I would need further information regarding the lengths of the sides of the triangles, the precise position of the points, and any angles that you've been given. Typically, in a geometry problem involving rotation, the lengths of the sides of the original triangle (triangle ABC) remain the same after the rotation, which means you can directly use those measures for the image triangle \( A'B'C' \).
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What is the length of side \( B'C' \)?
Since triangle \( A'B'C' \) is a rotation of triangle \( ABC \), the lengths of corresponding sides will be equal. If side \( BC \) in triangle \( ABC \) has a specific length (which you would need to provide), then the length of side \( B'C' \) will be equal to that length.
Length of side ( B'C' = BC = [value] \text{ units.}
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What is the measure of angle \( B \)?
Angles in a triangle also remain unchanged when the triangle is rotated. Therefore, if you provide the measure of angle \( A \) or angle \( C \), we can calculate angle \( B \) based on the property that the sum of the angles in a triangle is always 180 degrees.
If: \[ \text{Angle } A + \text{Angle } B + \text{Angle } C = 180^\circ \] You can determine angle \( B \) using: \[ \text{Angle } B = 180^\circ - (\text{Angle } A + \text{Angle } C) \]
Measure of angle ( B = [value] \text{ degrees.}
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What is the measure of angle \( C \)?
Similar to angle \( B \), if you know the measures of angles \( A \) and \( B \), you can find angle \( C \) using the same principle as mentioned above.
\[ \text{Angle } C = 180^\circ - (\text{Angle } A + \text{Angle } B) \]
Measure of angle ( C = [value] \text{ degrees.}
Feel free to fill in the specifics or provide any additional information needed, such as the actual lengths or angle measures from triangle \( ABC \), so I can assist you more accurately!