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

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

We wish to determine if the pair of triangles on the coordinate plane below are congruent.

Medium

1min

Outcomes

8.G.A.2

Explain that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. (Rotations are only about the origin and reflections are only over the y-axis and x-axis in Grade 8.)

3.04 Congruence transformations

Interactive practice questions

Outcomes

8.G.A.2

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