Translations and Congruence

  • 8th Grade
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| By Thames
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| Attempts: 20 | Questions: 20 | Updated: Dec 2, 2025
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Question 1 / 21
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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) Which statement is correct?

Explanation

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

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3) 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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4) Why are translations considered rigid motions?

Explanation

Rigid motions like translations keep size and shape unchanged.

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5) 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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6) 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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7) Which is true about translations on the coordinate plane?

Explanation

Translations shift lines without changing their slope.

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8) 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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9) Congruence under translation means:

Explanation

That’s what congruence under translation means.

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10) 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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11) 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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12) 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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13) 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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14) 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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15) 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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16) 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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17) 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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18) 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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19) 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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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...
Which statement is correct?
If a parallelogram is translated 10 units right, what happens to its...
Why are translations considered rigid motions?
The translation ⟨–5, 7⟩ applied to Q(4, –2) results in:
A trapezoid is moved 6 units left and 2 units down. What happens to...
Which is true about translations on the coordinate plane?
A translation is applied to a rectangle. Which measurements remain the...
Congruence under translation means:
Which of the following is true about translations and congruence?
Which transformation results in two figures that are always congruent?
Square ABCD has vertices A(0,0), B(2,0), C(2,2), D(0,2). It is...
Triangle XYZ has vertices at X(1,1), Y(4,1), Z(2,3). It is translated...
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'?
If point R(5, 7) → R'(–2, 10), what vector was used?
A figure undergoes a translation. Which property is changed?
A triangle is translated 4 units right. How does the translated...
If P(–3, 2) → P'(5, 2), what translation occurred?
Which transformation keeps figures congruent but reverses orientation?
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