Prove Figures Are Congruent With Transformations

In order to prove that two figures are congruent, I must show that I can map one to the other using the following transformations (select all that apply):

• Translation

• Rotation

• Reflection

• Dilation

Answer explanation

Congruent figures have the same shape AND size. This means all side lengths are equal. If a dilation is applied, that means the image and preimage are not the same size and therefore not congruent.

Coordinates A(8,6), B(2,-5), and C( -5,1) are connected to form ⧍ABC. If ⧍CDA is congruent to ⧍ABC, what are the coordinates of D?

• (1,12)

• (2,-1)

• (1,8)

• (2,7)

Determine if the two figures are congruent by using transformation. If so, what kind of transformation?

• congruent; a counterclockwise rotation of 90 degrees followed by a translation

• congruent; reflection

• congruent; translation

• not congruent

Which conclusions can be made? Select all that apply!

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True/False: a single rotation could map Triangle ABC onto Triangle A'B'C'.

• True

• False

Which of the following are congruence transformations? (select all that apply)

• Translations

• Dilations

• Rotations

• Reflections

Which of the following create congruent images? Select all that apply.

• Translations

• Reflections

• Rotations

• Dilation

For each pair of figures decide whether you can take figure A to figure B by a translation, a rotation, or a reflection.

• translation

• rotation

• reflection

What single transformation was applied to Figure A to get Figure B?

• Translation

• Rotation

• Reflection

T\left(x,y\right)\rightarrow\left(y,x\right) could represent a transformation that could establish congruence.

• True

• False