Congruence and Similarity

Lesson

In our previous lesson we learned how to identify if two shapes are congruent.

Using 3 forms of transformations, namely Turns, Flips and/or Slides (Rotations, Reflections and Translations) we can create congruent shapes. In fact all pairs of congruent shapes can be matched to each other using a series or one or more of the transformations turns, flips and slides.

Consider the figures shown

a) Are the two quadrilaterals similar, congruent or neither?

b) What type of transformation could have been used from quadrilateral ABCD to quadrilateral EFGH?

c) Identify the transformation from quadrilateral ABCD to quadrilateral EFGH.

Consider the quadrilateral with vertices at $A$`A` $\left(4,-2\right)$(4,−2), $B$`B` $\left(4,-6\right)$(4,−6), $C$`C` $\left(6,-6\right)$(6,−6) and $D$`D` $\left(6,-2\right)$(6,−2) and the quadrilateral with vertices at $E$`E` $\left(-4,-2\right)$(−4,−2), $F$`F` $\left(-4,-6\right)$(−4,−6), $G$`G` $\left(-6,-6\right)$(−6,−6) and $H$`H` $\left(-2,-2\right)$(−2,−2).

a) Are the two quadrilaterals similar, congruent or neither?

b) How could quadrilateral ABCD be transformed to form quadrilateral EFGH?

c) Identify which of the following transformations result in going from quadrilateral ABCD to quadrilateral EFGH.

Consider the transformation from $\left(x,y\right)$(`x`,`y`) to $\left(x,-y\right)$(`x`,−`y`).

What is the transformation?

Compare and apply single and multiple transformations

Analyse symmetrical patterns by the transformations used to create them

Apply transformation geometry in solving problems