Congruence and Similarity

Hong Kong

Stage 1 - Stage 3

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

Consider the figures shown.

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Are the two triangles congruent, similar or neither?

Congruent

ASimilar

BNeither

CWhat is the transformation from triangle $ABC$

`A``B``C`to triangle $A'B'C'$`A`′`B`′`C`′?Dilation

AReflection

BRotation

CTranslation

DWhat is the scale factor of the dilation from triangle $ABC$

`A``B``C`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?

congruent

Asimilar

Bneither

CWhat is the transformation from rectangle $ABCD$

`A``B``C``D`to rectangle $A'B'C'D'$`A`′`B`′`C`′`D`′?dilation

Areflection

Brotation

Ctranslation

DWhat is the scale factor of the dilation of rectangle $ABCD$

`A``B``C``D`to rectangle $A'B'C'D'$`A`′`B`′`C`′`D`′?

The quadrilateral with vertices at $\left(9,9\right)$(9,9), $\left(0,9\right)$(0,9), $\left(0,0\right)$(0,0) and $\left(9,0\right)$(9,0) is rotated 90 degrees clockwise around the origin and dilated by a factor of 2 with the origin as the centre of dilation.

What are the new coordinates of the vertices of the quadrilateral?

Write all four coordinates on the same line, separated by commas.