Congruent Figures Day 2.

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Presentation transcript:

Congruent Figures Day 2

Warm Up

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?

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.

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.

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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