In Changing Shapes, we looked at how congruent shapes may be transformed in one or more ways on a number plane. We can also transform similar shapes. These similar shapes will be dilated by a scale factor (ie. enlarged or reduced by a certain ratio) in addition to the transformation. The video attached to the examples below explains this process.

Examples

Question 1

Consider the figures shown.

Are the two triangles congruent, similar or neither?

Congruent

A

Similar

B

Neither

C

What is the transformation from triangle $ABC$ABC to triangle $A'B'C'$A′B′C′?

Dilation

A

Reflection

B

Rotation

C

Translation

D

What is the scale factor of the dilation from triangle $ABC$ABC to triangle $A'B'C'$A′B′C′?

Question 2

Consider the quadrilateral with vertices at $A$A$\left(-3,-3\right)$(−3,−3), $B$B$\left(-3,3\right)$(−3,3), $C$C$\left(3,3\right)$(3,3) and $D$D$\left(3,-3\right)$(3,−3), and the quadrilateral with vertices at $A'$A′$\left(-9,-9\right)$(−9,−9), $B'$B′$\left(-9,9\right)$(−9,9), $C'$C′$\left(9,9\right)$(9,9) and $D'$D′$\left(9,-9\right)$(9,−9).

Are the two rectangles similar, congruent or neither?

congruent

A

similar

B

neither

C

What is the transformation from rectangle $ABCD$ABCD to rectangle $A'B'C'D'$A′B′C′D′?

dilation

A

reflection

B

rotation

C

translation

D

What is the scale factor of the dilation of rectangle $ABCD$ABCD to rectangle $A'B'C'D'$A′B′C′D′?