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3.04 Congruence transformations

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

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
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Outcomes

8.G.2

Understand 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.

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