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India
Class IX

Transformations and Congruence

Interactive practice questions

Consider the figures shown.

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Two $triangle$triangle are placed on a Cartesian plane, where the x- and y- axes are labeled and range from -10 to 10. These $triangle$triangle, $ABC$ABC and $A'B'C'$ABC, have the same shape and size but are situated differently. The coordinates of the vertices are not explicitly given. The vertices of $triangle$triangle $ABC$ABC are located at A $\left(-2,3\right)$(2,3), B $\left(2,1\right)$(2,1), C $\left(4,-4\right)$(4,4), and D $\left(4,-4\right)$(4,4). Similarly, the vertices of $triangle$triangle $A'B'C'$ABC are positioned at A' $\left(1,5\right)$(1,5), B' $\left(5,3\right)$(5,3), C' $\left(7,-2\right)$(7,2), and D' $\left(7,-2\right)$(7,2).
a

Which term best describes the relationship between the two triangles ?

Congruent

A

Similar

B

Neither

C
b

What single transformation can take triangle $ABC$ABC to triangle $A'B'C'$ABC?

Reflection

A

Rotation

B

Translation

C

Dilation

D
c

Identify the transformation from triangle $ABC$ABC to triangle $A'B'C'$ABC.

A translation $2$2 units left and $3$3 units down.

A

A translation $3$3 units left and $2$2 units down.

B

A translation $2$2 units right and $3$3 units up.

C

A translation $3$3 units right and $2$2 units up.

D
Easy
1min

Consider the figures shown.

Easy
< 1min

Consider the quadrilateral with vertices at A(3, -1), B(1, -8), C(5, -8) and D(7, -1), and the quadrilateral with vertices at A'(-3, -1), B'(-1, -8), C'(-5, -8) and D'(-7, -1).

Easy
< 1min

Consider the transformation from $\left(x,y\right)$(x,y) to $\left(x-3,y-8\right)$(x3,y8).

Medium
< 1min
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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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