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 $A'B'C'$A′B′C′, 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 $A'B'C'$A′B′C′ 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).

Which term best describes the relationship between the two $triangle$ s ?

Congruent

Similar

Neither

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

Reflection

Rotation

Translation

Dilation

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

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

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

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

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

Easy

1min

Consider the figures shown.

Easy

< 1min

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

Easy

< 1min

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

Easy

< 1min

Outcomes

NC.M2.F-IF.1

Extend the concept of a function to include geometric transformations in the plane by recognizing that: • the domain and range of a transformation function f are sets of points in the plane; • the image of a transformation is a function of its pre-image.

NC.M2.F-IF.2

Extend the use of function notation to express the image of a geometric figure in the plane resulting from a translation, rotation by multiples of 90 degrees about the origin, reflection across an axis, or dilation as a function of its pre-image.

NC.M2.G-CO.2

Experiment with transformations in the plane. • Represent transformations in the plane. • Compare rigid motions that preserve distance and angle measure (translations, reflections, rotations) to transformations that do not preserve both distance and angle measure (e.G. Stretches, dilations). • Understand that rigid motions produce congruent figures while dilations produce similar figures.

NC.M2.G-CO.3

Given a triangle, quadrilateral, or regular polygon, describe any reflection or rotation symmetry i.E., Actions that carry the figure onto itself. Identify center and angle(s) of rotation symmetry. Identify line(s) of reflection symmetry.

NC.M2.G-CO.6

Determine whether two figures are congruent by specifying a rigid motion or sequence of rigid motions that will transform one figure onto the other.

NC.M2.G-SRT.1

Verify experimentally the properties of dilations with given center and scale factor:

NC.M2.G-SRT.1d

Dilations preserve angle measure.

NC.M2.G-SRT.2

Understand similarity in terms of transformations.

NC.M2.G-SRT.2a

Determine whether two figures are similar by specifying a sequence of transformations that will transform one figure into the other.

NC.M2.G-SRT.2b

Use the properties of dilations to show that two triangles are similar when all corresponding pairs of sides are proportional and all corresponding pairs of angles are congruent.

1.05 Transformations, congruence, and similarity

Interactive practice questions

Outcomes

NC.M2.F-IF.1

NC.M2.F-IF.2

NC.M2.G-CO.2

NC.M2.G-CO.3

NC.M2.G-CO.6

NC.M2.G-SRT.1

NC.M2.G-SRT.1d

NC.M2.G-SRT.2

NC.M2.G-SRT.2a

NC.M2.G-SRT.2b

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