Prove Figures Are Congruent With Transformations

Using transformations, prove that the two given figures are congruent: Rectangle PQRS with vertices P(1, 2), Q(1, 5), R(4, 5), S(4, 2) and Rectangle WXYZ with vertices W(1, 2), X(1, 5), Y(4, 5), Z(4, 2).

• Translate Rectangle PQRS by (0, 0) to coincide with Rectangle WXYZ

• Resize Rectangle PQRS to make it larger

• Reflect Rectangle PQRS over the x-axis

• Rotate Rectangle PQRS by 90 degrees

Are the figures congruent?

(What type of transformation is shown?)

• NOT Congruent (dilation)

• NOT Congruent (translation)

• Congruent (dilation)

• Congruent (translation)

Match the transformations to the triangles:

• Rotate 90 degrees counter-clockwise

• Rotate 270 degrees counter-clockwise

• Reflect over x=0

• Reflect over the y=0

• Reflect over the line y=4

Tags

CCSS.MATH.CONTENT.HSG.CO.A.5

Which types of transformations are congruent after the movement?

• Rotations

• Reflections

• Translations

• Dilations

Which transformation(s) create congruent figures?

• Dilation

• Translation

• Reflection

• Rotation

Which transformation was applied to figure A to form figure B?

• Figure A was reflected across line m to form figure B.

• Figure A was translated 8 units right and 6 units up to form figure B.

• Figure A was rotated 90° clockwise about point N to form figure B.

• Figure A was translated 6 units right and 8 units up to form figure B.

Which transformation does not produce an image that is congruent to the original?

• A dilation of scale factor 1 centered at (2,4)

• A dilation of scale factor ½ centered at the origin

• A reflection over y = 4x

• A rotation of 270 degrees followed by a translation down 2

For each pair of figures, decide whether you can take figure A to figure B by a translation, a rotation, or a reflection.

• translation

• rotation

• reflection

For each pair of figures, decide whether you can take figure A to figure B by translation, rotation or reflection.

• translation

• rotation

• reflection

What are the series of rigid motions that would map ∆ABC onto ∆A''B''C''?

• a reflection followed by a rotation

• a reflection followed by a translation

• a translation followed by a rotation

• a translation followed by a reflection