 # Transformations and congruence

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.

##### Question 1

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?

##### Question 2

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?

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

##### Question 3

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

What is the transformation?

### Outcomes

#### 10D.T1.02

Describe and compare the concepts of similarity and congruence