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Congruence and Similarity
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India
Class IX

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

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).

  1. Are the two rectangles similar, congruent or neither?

    congruent

    A

    similar

    B

    neither

    C

  2. 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

  3. 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

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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