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4.05 Transformations, congruence, and similarity

Interactive practice questions

Consider the figures shown.

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Two $triangle$triangle are placed on a Coordinate 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

$\Delta(FGH)$Δ(FGH) and $\Delta(F''G''H'')$Δ(FGH) are shown on the coordinate plane below.

Easy
< 1min

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

Easy
< 1min
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Outcomes

GEO-G.CO.2

Represent transformations as geometric functions that take points in the plane as inputs and give points as outputs. Compare transformations that preserve distance and angle measure to those that do not.

GEO-G.CO.3

Given a regular or irregular polygon, describe the rotations and reflections (symmetries) that map the polygon onto itself.

GEO-G.CO.6

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. Given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

GEO-G.SRT.1

Verify experimentally the properties of dilations given by a center and a scale factor.

GEO-G.SRT.2

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformations that similar triangles have equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

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