Congruence Through Translations

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Thames
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| Questions: 20 | Updated: Nov 24, 2025
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1) Which transformation best demonstrates that two polygons are congruent?

Explanation

A translation slides a figure without turning or resizing, so it shows congruence.

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About This Quiz
Congruence Through Translations - Quiz

Let's put it all together and prove figures match! In this quiz, you’ll use translations (and compare them with rotations and reflections) to show two polygons are congruent. You’ll write clear vector rules, map one figure to the other, and explain why translations are rigid motions—they move shapes without stretching,... see moreflipping, or turning their size or angles.
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2)
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2) If A(0, 4) → A'(0, –3), which translation vector is correct?

Explanation

From (0, 4) to (0, –3): x change = 0, y change = –3 – 4 = –7.

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3) Translations are considered what type of transformation?

Explanation

Translations are rigid motions. They keep lengths and angles the same.

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4) Which of the following does a translation NOT preserve?

Explanation

Translations preserve angles, orientation, and congruence. Only position changes.

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5) Triangle PQR has vertices at P(–1,2), Q(2,2), R(0,5). It is translated using ⟨–3, –2⟩. Where is Q'?

Explanation

Apply ⟨–3, –2⟩ to Q(2, 2): (2 – 3, 2 – 2) = (–1, 0).

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6) A translation moves a figure 6 units up and 4 units left. Which rule describes this?

Explanation

Left means subtract 4 from x. Up means add 6 to y.

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7) If translations preserve congruence, what is always true?

Explanation

Translations keep corresponding sides and angles equal, and images overlap after sliding.

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8) Which figure cannot be mapped onto its congruent copy by translation alone?

Explanation

A rotated copy needs a rotation, not just a translation.

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9) What vector maps D(7, –2) to D'(3, 4)?

Explanation

From (7, –2) to (3, 4): x change = 3 – 7 = –4, y change = 4 – (–2) = 6.

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10) Rectangle WXYZ has vertices at W(0,0), X(4,0), Y(4,3), Z(0,3). It is translated by (x, y) → (x + 2, y – 5). Where is Z'?

Explanation

Z(0, 3) → (0 + 2, 3 – 5) = (2, –2).

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11) Which statement is always true?

Explanation

They preserve size and shape.

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12) The translation ⟨8, –3⟩ is applied to E(–2, 7). Where is E'?

Explanation

E(–2, 7) + ⟨8, –3⟩ = (–2 + 8, 7 – 3) = (6, 4).

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13) Why do translations prove congruence?

Explanation

That is why a translation proves congruence.

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14) Which of the following transformations would not preserve congruence?

Explanation

Dilations change size, so they do not preserve congruence.

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15) Which vector moves a point 9 units down?

Explanation

Down 9 changes only y by –9.

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16) Pentagon JKLMP is translated by (x, y) → (x – 2, y + 4). Which is true about the image?

Explanation

Rule (x – 2, y + 4) shifts left 2 and up 4 with no size change.

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17) Which of the following describes two congruent figures?

Explanation

Reflections, translations, and rotations all map congruent figures.

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18) Translate A(5, 5) by ⟨–12, 0⟩. Where is A'?

Explanation

A(5, 5) + ⟨–12, 0⟩ = (–7, 5).

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19) A figure is congruent to its image after translation because:

Explanation

That is the defining property of translations.

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20) If T(–3, 9) → T'(–3, 0), what is the translation vector?

Explanation

From (–3, 9) to (–3, 0): x change = 0, y change = –9.

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Which transformation best demonstrates that two polygons are...
If A(0, 4) → A'(0, –3), which translation vector is correct?
Translations are considered what type of transformation?
Which of the following does a translation NOT preserve?
Triangle PQR has vertices at P(–1,2), Q(2,2), R(0,5). It is...
A translation moves a figure 6 units up and 4 units left. Which rule...
If translations preserve congruence, what is always true?
Which figure cannot be mapped onto its congruent copy by translation...
What vector maps D(7, –2) to D'(3, 4)?
Rectangle WXYZ has vertices at W(0,0), X(4,0), Y(4,3), Z(0,3). It is...
Which statement is always true?
The translation ⟨8, –3⟩ is applied to E(–2, 7). Where is E'?
Why do translations prove congruence?
Which of the following transformations would not preserve congruence?
Which vector moves a point 9 units down?
Pentagon JKLMP is translated by (x, y) → (x – 2, y + 4). Which is...
Which of the following describes two congruent figures?
Translate A(5, 5) by ⟨–12, 0⟩. Where is A'?
A figure is congruent to its image after translation because:
If T(–3, 9) → T'(–3, 0), what is the translation vector?
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