Translations and Congruence

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| Questions: 20 | Updated: Nov 24, 2025
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1) Which of the following is the definition of congruence using transformations?

Explanation

That’s the definition of congruence using rigid motions.

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About This Quiz
Translations And Congruence - Quiz

Want to see why translated figures are still a perfect match? In this quiz, you’ll connect translations to congruence: same size, same shape—just a new position. You’ll decide what changes (position) and what doesn’t (lengths, angles, slopes), and use translations to show two shapes are congruent without measuring every side.

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2) The translation ⟨–5, 7⟩ applied to Q(4, –2) results in:

Explanation

Apply ⟨–5, 7⟩ to (4, –2): (4 – 5, –2 + 7) = (–1, 5).

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3) Which statement is correct?

Explanation

If one figure maps exactly onto another by translation, they’re congruent.

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4) If a parallelogram is translated 10 units right, what happens to its congruence?

Explanation

Moving a parallelogram doesn’t alter its shape or size.

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5) Why are translations considered rigid motions?

Explanation

Rigid motions like translations keep size and shape unchanged.

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6) Which of the following is true about translations and congruence?

Explanation

Translations move a figure without changing its dimensions or form.

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7) A figure undergoes a translation. Which property is changed?

Explanation

Only the figure’s location changes; shape, size, and orientation remain unchanged.

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8) A trapezoid is moved 6 units left and 2 units down. What happens to its side lengths?

Explanation

Translations don’t change side lengths; only the position changes.

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9) Triangle XYZ has vertices at X(1,1), Y(4,1), Z(2,3). It is translated using (x, y) → (x + 2, y – 1). Where is Z'?

Explanation

Z(2, 3) → (2 + 2, 3 – 1) = (4, 2).

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10) Which is true about translations on the coordinate plane?

Explanation

Translations shift lines without changing their slope.

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11) If figure A is congruent to figure B, which must be true?

Explanation

Congruent figures can be related by a translation, reflection, or rotation.

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12) Point M(–2, 3) is translated by vector ⟨4, –5⟩. Where is M'?

Explanation

Add ⟨4, –5⟩ to (–2, 3): (–2 + 4, 3 – 5) = (2, –2).

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13) A translation is applied to a rectangle. Which measurements remain the same?

Explanation

Side lengths, angles, and diagonals all stay the same after a translation.

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14) If point R(5, 7) → R'(–2, 10), what vector was used?

Explanation

From (5, 7) to (–2, 10): x decreases by 7, y increases by 3.

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15) Congruence under translation means:

Explanation

That’s what congruence under translation means.

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16) A triangle is translated 4 units right. How does the translated triangle compare to the original?

Explanation

A translation keeps the triangle’s size and shape the same, so it stays congruent.

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17) Which transformation results in two figures that are always congruent?

Explanation

A translation produces figures that are exactly congruent to the original.

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18) If P(–3, 2) → P'(5, 2), what translation occurred?

Explanation

x changes from –3 to 5 (an increase of 8); y stays the same.

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19) Square ABCD has vertices A(0,0), B(2,0), C(2,2), D(0,2). It is translated 3 units right and 1 unit up. Where is A'?

Explanation

Move A(0, 0) three units right and one unit up: (0 + 3, 0 + 1) = (3, 1).

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20) Which transformation keeps figures congruent but reverses orientation?

Explanation

A reflection flips a figure, keeping size but reversing orientation.

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Which of the following is the definition of congruence using...
The translation ⟨–5, 7⟩ applied to Q(4, –2) results in:
Which statement is correct?
If a parallelogram is translated 10 units right, what happens to its...
Why are translations considered rigid motions?
Which of the following is true about translations and congruence?
A figure undergoes a translation. Which property is changed?
A trapezoid is moved 6 units left and 2 units down. What happens to...
Triangle XYZ has vertices at X(1,1), Y(4,1), Z(2,3). It is translated...
Which is true about translations on the coordinate plane?
If figure A is congruent to figure B, which must be true?
Point M(–2, 3) is translated by vector ⟨4, –5⟩. Where is M'?
A translation is applied to a rectangle. Which measurements remain the...
If point R(5, 7) → R'(–2, 10), what vector was used?
Congruence under translation means:
A triangle is translated 4 units right. How does the translated...
Which transformation results in two figures that are always congruent?
If P(–3, 2) → P'(5, 2), what translation occurred?
Square ABCD has vertices A(0,0), B(2,0), C(2,2), D(0,2). It is...
Which transformation keeps figures congruent but reverses orientation?
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