In this topic, students will:
understand translations
translate a figure on a coordinate plane
describe a translation
understand and describe a reflection
reflect two-dimensional figures
identify and perform a rotaion
determine how a rotation affects a two-dimensional figure
understand a sequence of transformations
describe and perform a sequence of transformations
understand congruence of figures using a series of transformations
identify congruent figures
understand dilations
dilate to enlarge or reduce a figure in a coordinate plane
understand similarity
complete a similarity transformation
identify similar figures
understand the relationships of angles formed by parallel lines and a transversal
find unknown angle measures
understand the relationship of the interior angles of a triangle
find unknown angle measures
determine whether triangles are similar
Vocabulary:
Transformation - a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system
Translation - a transformation of a shape in a plane that preserves length, which means that the object is transformed without getting its dimensions affected.
Image - the image of a function is the set of all output values it may produce
Reflection - reflected figures are the same distance from the line of reflection but on opposite sides
Line of reflection - a reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.
Rotation - turns a figure about a fixed point, called the center of rotation. The angle of rotation is the number of degrees the figure is rotated.
Angle of rotation - the number of degrees the figure is rotated
Center of rotation - a point about which a plane figure rotates
Congruent - two figures are congruent if a sequence of transformations maps one figure onto the other
Dilation - a dilation results in an image that is the same shape but not the same size as the preimage.
Scale factor - the ratio between corresponding measurements of an object and a representation of that object
Enlargement - a type of transformation where we change the size of the original shape to make it bigger by multiplying it by a scale factor
Reduction - a transformation of an object that has the same shape, but decreases in size of the object
Similar - similar figures have congruent angles but can be different sizes
Transversal - a line that passes between two parallel lines at an angle that creates additional angles on the parallel lines
Corresponding angles - angles lie on the same side of the transversal and in corresponding positions
Alternate interior angles - the two angles inside of parallel lines on opposite sides of the transversal line
Same-side interior angles - angles that lie within a pair of lines and on the same side of a transversal
Remote interior angles - two adjacent interior angles corresponding to each exterior angle of a triangle
Exterior angle of a triangle - formed by a side and an extension of an adjacent side of a triangle