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Congruent Figures Day 2
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Warm Up
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Graph triangle ABC with vertices A(-1, 1), B(-3, 2), and C(-3, 1)
Graph triangle ABC with vertices A(-1, 1), B(-3, 2), and C(-3, 1). Then perform the following series of transformations, in order, on triangle ABC. (1) Rotate the triangle 90° clockwise. (2) Reflect the rotated triangle over the x-axis. (3) Translate the reflected triangle 3 units left and 1 unit up. What are the coordinates of the vertices of the final image?
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If there exists a sequence of translations, reflections, and/or rotations that will transform one figure into the other, the two figures are congruent. Note that dilations are not included in this list of transformations. The image after a dilation is either an enlargement or reduction of the original figure, making the two figures similar but not congruent. While dilations preserve the shape of a figure, they do not preserve the size. A dilation is often called a similarity transformation.
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How do you know if a two dimensional figure is congruent to another
How do you know if a two dimensional figure is congruent to another? Two figures are congruent if the second can be obtained from the first by a sequence of rotations, reflections, and translations. The two figures will have the same size and shape.
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When two figures have different orientations, what clues help you decide which transformations were performed in the sequence of transformations? In order to get a turned image, a rotation must have occurred. In order to get a mirror image, a reflection must have occurred.
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