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27 Cards in this Set
- Front
- Back
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In geometry, what is a translation?
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A translation is the movement of a shape without any rotation. A shape's points all slide the same distance and direction.
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In geometry, what is a rotation?
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A rotation is the moving of a shape around a central point or axis. Rotations are usually measured in degrees.
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In geometry, what is a reflection?
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A reflection is a change that flips a shape across a line.
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In geometry, what is a dilation?
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A dilation is a transformation in which a figure is enlarged or reduced using a scale factor that is not equal to zero, without altering the center.
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Are these two triangles congruent? If so, what was done to the first triangle to obtain the second?
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The triangles are congruent. The first triangle was reflected over a straight line below it to obtain the second triangle. (The first triangle was rotated 180 degrees to obtain the second triangle is an equally correct solution.)
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Are these two trapezoids congruent? If so, what was done to the first trapezoid to obtain the second?
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The trapezoids are congruent. The first trapezoid was reflected over a vertical line to the right of the figure to obtain the second. (Student may say it was reflected over the y-axis from quadrant IV to quadrant I; this is equally accurate.)
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Are these two rectangles congruent? If so, what was done to the first rectangle to obtain the second?
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The rectangles are not congruent.
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Are these two rectangles congruent? If so, what was done to the first rectangle to obtain the second?
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The rectangles are congruent. The first was translated (or slid) to the right to obtain the second.
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This picture shows two congruent rectangles. Show that the rectangles are congruent by finding a translation followed by a rotation which maps one of the rectangles to the other.
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This can be done by translating a vertex of rectangle 1 to a corresponding vertex of rectangle 2, then rotating it counterclockwise by approximately 50 degrees.
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This picture shows two congruent rectangles. Explain why the congruence of the two rectangles cannot be shown by only translating Rectangle 1 to Rectangle 2.
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A translation can move rectangle 1 to any other position on the coordinate grid but will not influence the angles its sides make with the grid lines. The lines containing the upper and lower sides of the rectangle will always be parallel to the horizontal lines on the grid and the lines containing the left and right sides of the rectangle will always be parallel to the vertical lines in the grid. Since none of the lines containing sides of rectangle 2 are parallel to the grid lines, rectangle 1 cannot be moved to rectangle 2 with a translation.
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This picture shows two congruent rectangles. Can the congruence of the two rectangles be shown with a single reflection? Explain.
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The congruence cannot be shown with a single reflection. No line can be drawn that will create a mirror image of rectangle 1 that appears as rectangle 2.
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Graph the image of parallelogram ABCD after dilation with a scale factor of 3, centered at the origin.
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Describe the effect of the dilation of the parallelogram. How did you figure out where to plot the points?
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The dilation increased the size of the parallelogram. Its side lengths are in ratio to the corresponding sides in the original figure. I multiplied the coordinates of the points by 3 to find the new coordinates for the corners of the parallelogram.
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What will be the coordinates of point M if it is translated 5 units down and 2 units to the right?
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(1, -2)
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Rotate this shape 90 degrees counterclockwise about the origin (0,0).
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Rotate this shape 180 degrees about the origin.
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Draw a reflection of ∆ ABC over the line x=-2. Label the image of A as A', the image of B as B' and the image of C as C'.
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Describe the effect of the reflections of ∆ ABC over the line x=-2. Did any features of the triangle change?
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The reflection of the triangle over the line x=-2 was a horizontal flip of the triangle. All features of the triangle (shape, size, angle measure) were conserved by this transformation.
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a 2-d figure is similar to another if the second can be obtained from the first by a sequence of what 4 transformations?
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Rotations, Reflections, Translations and Dilations
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Which two figures are similar? Explain their similarity.
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Figures A and C are simliar. Figure C is a dilation of figure A with a scale factor of 2.
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Explain the sequence that exhibits the similarity between these two figures.
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Reflection over the line x= -6 followed by a translation down two units.
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Explain the sequence that exhibits the similarity between figures A & B.
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Reflection over the x-axis followed by a dilation with a scale factor of 0.5
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Given that line DE is parallel to line AC in this diagram, prove that a+b+c=180.
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Since line AB is a transversal of parallel lines DE and AX, we have the equality of alternate interior angles. ∠DBA=a
Using the transversal BC of the same lines, we have the equality of alternate interior angles ∠EBC=c Since angles ∠DBA, ∠EBC, and ∠ABC, form a straight line, we can conclude that 180=<DBA+<ABC+<EBC Therefore, by substitution, 180=a+b+c |
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The measure of an exterior angle of a triangle is equal to what?
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The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle.
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In this diagram, the horizontal lines are parallel and cut by a transversal. Which angles are alternate interior angles?
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angles 4 and 6 and angles 3 and 5
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In this diagram, the horizontal lines are parallel and cut by a transversal. Which angles are corresponding?
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Angles 1 and 5, angles 2 and 6, angles 3 and 7, angles 4 and 8
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Two triangles are similar if they have all of their __________ equal.
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Two triangles are similar if they have all of their angles equal.
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