When triangle LMN is reflected across the y-axis to create triangle L'M'N', there are several key observations about the properties of the triangles:
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Corresponding Angles: The measures of corresponding angles in triangle LMN and triangle L'M'N' will be equal. This is because reflection is a rigid transformation that preserves angle measures.
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Lengths of Corresponding Sides: The lengths of corresponding sides in both triangles will also be the same. Again, this is a property of rigid transformations, which maintain distances.
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X-coordinates of Corresponding Vertices: When a point (x, y) is reflected across the y-axis, its image becomes (-x, y). Hence, the x-coordinates of the corresponding vertices will have opposite signs. For example, if the vertices of triangle LMN are L(x₁, y₁), M(x₂, y₂), and N(x₃, y₃), then the vertices of triangle L'M'N' will be L'(-x₁, y₁), M'(-x₂, y₂), and N'(-x₃, y₃).
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Y-coordinates of Corresponding Vertices: The y-coordinates of the corresponding vertices will remain unchanged during the reflection across the y-axis. So, if vertex L has coordinates (x₁, y₁), then vertex L' will have coordinates (-x₁, y₁).
In summary, reflecting triangle LMN across the y-axis results in triangle L'M'N' which has:
- Equal corresponding angles.
- Equal lengths of corresponding sides.
- X-coordinates that change sign.
- Y-coordinates that remain the same.