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.
Consider the figures shown.
Are the two triangles congruent, similar or neither?
What is the transformation from triangle $ABC$ABC to triangle $A'B'C'$A′B′C′?
What is the scale factor of the dilation from triangle $ABC$ABC to triangle $A'B'C'$A′B′C′?
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?
What is the transformation from rectangle $ABCD$ABCD to rectangle $A'B'C'D'$A′B′C′D′?
What is the scale factor of the dilation of rectangle $ABCD$ABCD to rectangle $A'B'C'D'$A′B′C′D′?
Verify, through investigation, the properties of similar triangles