7-10 6th grade math Transformations

Objective To identify translations, rotations, and reflections of two-dimensional figures Why? To know how shapes are transformed, or moved, in a plane or in space. Transformational geometry = motion geometry.

California State Standards MG 3.2 (Gr. 7): Understand … simple figures, … and determine their images under translations and reflections. MG 2.0: Identify and describe the properties of two-dimensional figures. MG 2.3: Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle)

Vocabulary Translation Rotation Reflection Line symmetry The turning, sliding, of a plane figure. Every point of the figure slides the same distance in the same direction. Rotation A transformation obtained by rotating, turning, a figure through a given angle about a point. Every point of the figure is rotated (clockwise or counter-clockwise) at the same angle around a point in the same direction. Reflection The mirror image, a flipping, of a figure about a line of symmetry. Each point of the reflected image is the same distance from the line as the corresponding point of the original figure. After a move or combination of moves, the figure preserves its shape and size and is congruent to the original figure. Line symmetry A line that divides a figure in half into two congruent parts when folded. Some transformations may be in multiple steps.

Translation The turning, sliding, of a plane figure. Every point of the figure slides the same distance in the same direction. B ┐ E A C D ┐ F

Rotations usually share a point of rotation. A transformation obtained by rotating, turning, a figure through a given angle about a point. Every point of the figure is rotated (clockwise or counter-clockwise) at the same angle around a point in the same direction. B A C D E Rotations usually share a point of rotation.

Reflection Line symmetry The mirror image, a flipping, of a figure about a line of symmetry. Each point of the reflected image is the same distance from the line as the corresponding point of the original figure. After a move or combination of moves, the figure preserves its shape and size and is congruent to the original figure. Line symmetry A line that divides a figure in half into two congruent parts when folded.

Line symmetry A line that divides a figure in half into two congruent parts when folded. Not to be confused with diagonals (corner to corner) 2 lines of symmetry 4 lines of symmetry Some figures has more than one line of symmetry, where some have 0 lines of symmetry.

How to Find Transformations 1)Observe the transformation 2) Look for the common angles and/or sides. Ask yourself: how did this move? 3) If transformation is touching, rotation. If apart, reflection or translation. 4) If transformation is in same layout, translation. 5) If transformation seems opposite or like a mirror, reflection. 1) x y Reflection 2) Translation 3) Reflection, rotation

How to Find Lines of Symmetry 2 lines of symmetry 1 line of symmetry 4 lines of symmetry Observe figure Be sure to ‘cut’ figure and to have equal parts. Like folds. Try folding on the drawn lines of symmetry.

Try It! Reflection Rotation Identify transformation 1) 2) 3) Reflection, translation Identify transformation 1) 2) 3)

Try One More! Sketch a triangle with 3 lines of symmetry

Objective Review To identify translations, rotations, and reflections of two-dimensional figures Why? You now know how shapes are transformed, or moved, in a plane or in space. Transformational geometry = motion geometry. You can translate (slide), rotate (turn), or reflect (flip) a figure to a different position, but still have the same shape and size. Figures may have one or more lines of symmetry or none.

Independent Practice Complete problems 5-11 Copy original problem first. Show all work! If time, complete Mixed Review: 12-16 If still more time, work on Accelerated Math.