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connexus.com/assessments/elm.aspx?idAssessment=\&idWebuser=\&idSection=\&close=true\&popup=trueGeom B Unit Test*Which of the following are examples of isometries? Pick all that apply. ( point)(I) parallelogram parallelogram (II) hexagon hexagon (III) triangle triangle
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Q. connexus.com/assessments/elm.aspx?idAssessment=\&idWebuser=\&idSection=\&close=true\&popup=trueGeom B Unit Test*Which of the following are examples of isometries? Pick all that apply. ( point)(I) parallelogram parallelogram (II) hexagon hexagon (III) triangle triangle
- Define Isometry: Identify the definition of an isometry. An isometry is a transformation in geometry that preserves distances between points, which means the shape's size and form remain unchanged after the transformation. Examples of isometries include translations, rotations, reflections, and glide reflections.
- Analyze Parallelogram Transformation: Analyze option (I): A parallelogram transformed to parallelogram . To be an isometry, the corresponding sides and angles of the parallelograms must be congruent. Since the problem statement does not provide specific measurements or angles, we cannot confirm that this is an isometry based solely on the given information. However, if the transformation preserves side lengths and angles, then it would be an isometry.
- Analyze Hexagon Transformation: Analyze option (II): A hexagon transformed to hexagon . Similar to option (I), for this to be an isometry, the corresponding sides and angles of the hexagons must be congruent. Again, without specific measurements or angles, we cannot confirm that this is an isometry based on the given information alone. However, if the transformation preserves side lengths and angles, then it would be an isometry.
- Analyze Triangle Transformation: Analyze option (III): A triangle transformed to triangle . Triangles are simpler figures, and any transformation that maps one triangle to another while preserving side lengths and angles is an isometry. This includes translations, rotations, and reflections. Since triangles have fewer sides and angles to consider, it is more likely that this transformation is an isometry, assuming that side lengths and angles are preserved.
- Determine Isometries: Determine which transformations are isometries. Based on the information given, we cannot definitively say that options (I) and (II) are isometries without additional information about the preservation of side lengths and angles. However, option (III) is likely to be an isometry if it preserves the side lengths and angles of the triangle.
