Explain: To show congruence a transformation of both______ and_______must be completed because
To show congruence, a transformation of both the shape and its size must be completed. Congruence refers to the property of two shapes being identical in size and shape. This means that all corresponding sides and angles of the shapes are equal.
Transforming the shape ensures that the two shapes have the same shape or outline. This can be achieved by rotating, reflecting, or translating one shape to match the orientation of the other. The transformation should preserve the overall shape of the original figure.
Transforming the size ensures that the two shapes have the same dimensions or proportions. This can be achieved by scaling the original figure uniformly or non-uniformly, either magnifying or reducing its size. In this transformation, the overall shape of the original figure is retained while its dimensions are adjusted accordingly.
Both transformations are necessary to show congruence because simply resizing the shape or merely changing its orientation would not guarantee that the corresponding sides and angles of the two shapes match. By completing both transformations, we can ensure that the shapes are not only identical in appearance but also have the same proportions and dimensions, thus demonstrating congruence.
Explain: To show congruence a transformation of both ______ and ______ must be completed because
To show congruence, a transformation of both the shape and its position must be completed. Congruence means that two shapes are exactly the same in size and shape, with corresponding angles and sides that match.
Transforming the shape involves altering the dimensions and proportions of the original shape while preserving its orientation or position. This can be achieved through scaling (enlarging or reducing), stretching, or shearing the shape to match the desired size and proportions. It is important to note that the shape's angles and sides must remain unchanged during this transformation.
Transforming the position involves moving or relocating the shape while maintaining its size and proportions. This can be done through translation (shifting), rotation, or reflection. The goal is to align the shape's position with a reference point or another shape, ensuring that their corresponding angles and sides match.
Completing both transformations is crucial to demonstrate congruence because simply changing the shape's position without adjusting its dimensions would result in two shapes that may have the same angles and sides but different sizes. Similarly, altering the shape's dimensions without adjusting its position would lead to two shapes with the same size but different orientations. By completing both transformations, we ensure that the shapes are not only identical in appearance but also have the same dimensions, proportions, and positions, thus showcasing congruence.
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Explain: To show congruence a transformation of both ______ and ______ must be completed because