Topics
9. Transformations & Congruence
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Math 1

9.05 Congruence transformations

Lesson
Practice

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 $A'B'C'$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).
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 $A'B'C'$A′B′C′?

Reflection

A

Rotation

B

Translation

C

Dilation

D
c

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

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

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.

G-CO.7

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

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