Transformations and Similarity

Lesson

Practice

Lesson

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.

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Two triangles are depicted on a Cartesian coordinate plane with x and y-axes ranging from -10 to 10. The larger triangle, labeled with vertices A' $\left(-6,-2\right)$(−6,−2), B' $\left(2,6\right)$(2,6), and C' $\left(6,-6\right)$(6,−6), is shaded in light gray. The smaller triangle, labeled with vertices A $\left(-3,-1\right)$(−3,−1), B $\left(1,3\right)$(1,3), and C $\left(3,-3\right)$(3,−3), is shaded in dark gray and positioned inside the larger triangle. Although they share the same shape, the triangles differ in size

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′?

Question 3

Outcomes

MS1-12-3

interprets the results of measurements and calculations and makes judgements about their reasonableness

MS1-12-4

analyses two-dimensional and three-dimensional models to solve practical problems