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India
Class IX

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?

c) Identify the transformation 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?

 

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. 

 

Question 3

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

What is the transformation?

 

Outcomes

9.G.T.1

Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence). Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

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