7-106th 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– 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

• 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– 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 Transformations1)Observe the

transformation2) 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

Reflection2)

Translation3)

Reflection, rotation

How to Find Lines of Symmetry1) Observe figure2) Be sure to ‘cut’ figure

and to have equal parts. Like folds.

3) Try folding on the drawn lines of symmetry.

2 lines of symmetry

1 line of symmetry

4 lines of symmetry

Try It!Identify transformation1)

2)

3)

1) Reflection

2) Rotation

3) Reflection, translation

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.