Translations And Congruence

1) Which of the following is the definition of congruence using transformations?

Two figures are congruent if one can be transformed into the other using only translations, reflections, or rotations

Two figures are congruent if they look the same size

Two figures are congruent if one is a dilation of the other

Two figures are congruent if their areas are equal

That’s the definition of congruence using rigid motions.

Explanation

That’s the definition of congruence using rigid motions.

2) Which statement is correct?

Translations can prove congruence between two figures

Translations change side lengths but not angles

Translations distort figures

Translations always reverse orientation

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

Explanation

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

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

It is not congruent anymore

It becomes larger

It remains congruent

It becomes reflected

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

Explanation

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

4) Why are translations considered rigid motions?

They shrink figures

They preserve congruence

They distort angles

They rotate figures

Rigid motions like translations keep size and shape unchanged.

Explanation

Rigid motions like translations keep size and shape unchanged.

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

(–9, –9)

(–1, 5)

(–1, –9)

(9, 5)

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

Explanation

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

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

They decrease

They increase

They remain the same

They double

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

Explanation

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

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

Side lengths

Angle measures

Diagonals

All of the above

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

Explanation

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

8) Congruence under translation means:

Figures have the same size, shape, and orientation

Figures have the same area but different shapes

Figures are enlargements of one another

Figures overlap completely after dilation

That’s what congruence under translation means.

Explanation

That’s what congruence under translation means.

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

Translations preserve size but not shape

Translations preserve both size and shape

Translations preserve only orientation

Translations change lengths but preserve angles

Translations move a figure without changing its dimensions or form.

Explanation

Translations move a figure without changing its dimensions or form.

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

Translation

Dilation

Stretching

Enlargement

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

Explanation

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

11) 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'?

(0, 1)

(3, 1)

(3, 0)

(1, 3)

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

Explanation

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

12) 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'?

(2, 2)

(4, 2)

(0, 2)

(2, –1)

Z(2, 3) → (2 + 2, 3 – 1) = (4, 2).

Explanation

Z(2, 3) → (2 + 2, 3 – 1) = (4, 2).

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

They change slopes of lines

They preserve slopes of lines

They double slopes of lines

They reverse slopes of lines

Translations shift lines without changing their slope.

Explanation

Translations shift lines without changing their slope.

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

There is a rigid motion that maps A to B

A is smaller than B

B is a dilation of A

A is a reflection of B

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

Explanation

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

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

(–6, –2)

(2, –2)

(2, 8)

(–6, 8)

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

Explanation

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

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

⟨–7, 3⟩

⟨7, 3⟩

⟨–3, –7⟩

⟨–7, –3⟩

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

Explanation

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

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

Position

Orientation

Distance between points

Shape

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

Explanation

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

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

The triangles are similar but not congruent

The triangles are congruent

The translated triangle is larger

The translated triangle is reflected

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

Explanation

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

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

⟨8, 0⟩

⟨–8, 0⟩

⟨0, 8⟩

⟨0, –8⟩

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

Explanation

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

20) Which transformation keeps figures congruent but reverses orientation?

Reflection

Translation

Rotation

None

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

Explanation

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

Translations and Congruence

1) Which of the following is the definition of congruence using transformations?

2)

What first name or nickname would you like us to use?

2) Which statement is correct?

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

4) Why are translations considered rigid motions?

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

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

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

8) Congruence under translation means:

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

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

11) 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'?

12) 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'?

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

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

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

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

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

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

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

20) Which transformation keeps figures congruent but reverses orientation?