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What is a translation?
A translation is a transformation that moves every point of a figure the same distance and the same direction.
What is a rotation?
A rotation is a transformation that turns around a fixed point, called the center of rotation.
What does it mean when figure is congruent?
It means the figure has the same size and shape as another figure.
What does it mean when figures are similar?
It means that you can map one figure to the other by a sequence of rotations, reflections, translations, and dilations.
What is a exterior angle of a triangle?
An exterior angle of a triangle is an angle formed by a side and an extension of an adjacent angle.
What is a reflection?
A reflection is a transformation that flips a figure over a line of reflection.
What does transformation mean?
A transformation is a change in the position, shape, or size of a figure.
What does a dilation mean?
A dilation means a transformation that moves each point along the way through the point, starting from a scale factor.
What is a transversal?
A transversal is a line that intersects two or more lines at different points.
What is a remote interior angle?
A remote interior angle is the two nonadjacent interior angles of a triangle with an exterior angle.
The points of QRST are Q(-2,-4), R(-1,-6), S(-1,0), and T(-2,2). What are the points of Q'R'S'T' as reflected across the y-axis?
The points are Q'(2,-4), R'(1,-6), S'(1,0), and T'(2,2).
The coordinates of the rectangle ABCD are A(3,-2), B(3,2), C(-3,2), and D(-3,-2). Rectangle ABCD is rotated 90 degrees about the origin. What are the coordinates of rectangle A'B'C'D'?
The coordinates of A'B'C'D' are A'(2,3), B'(-2,3), C'(-2,-3), and D'(2,-3).
What is the difference of enlargement and reduction, as used to find dilations?
The difference is that enlargement is a dilation with a scale factor greater than 1, while reduction is a dilation with a scale factor between 0 and 1.
If a figure is similar to another figure, is it also a congruent figure? Explain.
No, because when it's similar it can be mapped by every transformation, however when it's congruent it can be mapped by every transformation except dilations.
Are the triangles similar to two interior angle for one triangle 94 degrees and 45 degrees, and the other triangles other interior angles are 94 degrees and 65 degrees? Explain.
No because the two angles of one are not congruent to two angles of the other triangles, also known as the Angle-Angle (AA) Criterion.
The points of ABC are A(2,2), B(4,4), and C(6,3). What are the points of A'B'C' after ABC is translated 4 units down and 5 units to the left?
The points of A'B'C' are A'(-3,-2), B'(-1,0), and C'(1,-1).
The coordinates of STUV are S(-4,-2), T(-2,-2), U(-2,-4), and V(-4,-4). What is the image of STUV after a 270 degree rotation about the origin?
The coordinates of the image is S'(-2,4), T'(-2,2), U'(-4,2), and V'(-4,4).
The coordinates of the parallelogram ABCD are A(-4,1), B(0,1), C(1,-1), and D(-3,-1). What are the coordinates of the image of the parallelogram ABCD after a dilation with center (0,0) and a scale factor of 3?
What types of angles are corresponding angles, alternate interior angles, and same-side interior angle? Are they congruent angles or supplementary?
Corresponding and alternate interior angles are congruent angles, however same-side interior angles are supplementary.
If the remote interior angles are 85 and 65, and the exterior angle of a triangle is 150, what is the other interior angle?
The other interior angle is 30 degrees.
Points XYZ are X(3,6), Y(5,7), Z(4,-1). What are the points of X'Y'Z' when they are reflected across X=-1?
The points of X'Y'Z' are X'(-5,6), Y'(-7,7), and Z'(-6,-1)
When the coordinates of the rectangle ABCD are A(-5,4), B(-1,4), C(-1,2), D(-5,2), what is the image after it was translated 5 units down, followed by a reflection across the y-axis?
The coordinates are A"(5,-1), B"(1,-1),C"(1,-3), and D"(5,3).
What is the scale factor of GFDE to G'F'D'E if the coordinates are G(0,6), F(5,6), D(0,0), and E(5,0) and G'(0,18), F'(15,18), D'(0,0), E'(15,0)?
The scale factor is 3.
If g ll h, what must x equal if 90 degrees and (8x+2) are the same-side interior angles?
If g ll h, x must equal 11.
If two remote interior angles are 3x and 2x, and the exterior angle is 115, what is x?