Congruence Through Translations

1) Which transformation best demonstrates that two polygons are congruent?

Translation

Stretching

Scaling

Shearing

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

Explanation

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

2) If A(0, 4) → A'(0, –3), which translation vector is correct?

⟨0, –7⟩

⟨0, 7⟩

⟨–7, 0⟩

⟨7, 0⟩

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

Explanation

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

3) Translations are considered what type of transformation?

Rigid

Non-rigid

Distorting

Enlarging

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

Explanation

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

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

Angle measures

Orientation

Position

Congruence

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

Explanation

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

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

(–1, 0)

(–1, –4)

(5, 0)

(–5, 0)

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

Explanation

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

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

(x, y) → (x + 4, y – 6)

(x, y) → (x – 4, y + 6)

(x, y) → (x + 6, y – 4)

(x, y) → (x – 6, y + 4)

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

Explanation

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

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

Corresponding sides are equal

Corresponding angles are equal

Figures overlap exactly after translation

All of the above

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

Explanation

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

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

A rotated square

A translated triangle

A shifted circle

A moved parallelogram

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

Explanation

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

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

⟨–4, 6⟩

⟨4, –6⟩

⟨–10, 6⟩

⟨6, –4⟩

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

Explanation

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

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'?

(2, –2)

(–2, –5)

(2, 8)

(–2, 8)

Z(0, 3) → (0 + 2, 3 – 5) = (2, –2).

Explanation

Z(0, 3) → (0 + 2, 3 – 5) = (2, –2).

11) Which statement is always true?

Translations change figure size

Translations create congruent figures

Translations flip figures over lines

Translations distort shapes

They preserve size and shape.

Explanation

They preserve size and shape.

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

(10, 4)

(6, 4)

(–10, 10)

(–10, 4)

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

Explanation

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

13) Why do translations prove congruence?

They change distances equally

They preserve lengths and angles exactly

They distort orientation

They shrink figures proportionally

That is why a translation proves congruence.

Explanation

That is why a translation proves congruence.

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

Translation

Rotation

Reflection

Dilation

Dilations change size, so they do not preserve congruence.

Explanation

Dilations change size, so they do not preserve congruence.

15) Which vector moves a point 9 units down?

⟨9, 0⟩

⟨0, –9⟩

⟨–9, 0⟩

⟨0, 9⟩

Down 9 changes only y by –9.

Explanation

Down 9 changes only y by –9.

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

It is not congruent

It is congruent and moved left and up

It is larger

It is rotated

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

Explanation

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

17) Which of the following describes two congruent figures?

One is the reflection of the other

One is the translation of the other

One is the rotation of the other

All of the above

Reflections, translations, and rotations all map congruent figures.

Explanation

Reflections, translations, and rotations all map congruent figures.

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

(–7, 5)

(7, 5)

(17, 5)

(–17, 5)

A(5, 5) + ⟨–12, 0⟩ = (–7, 5).

Explanation

A(5, 5) + ⟨–12, 0⟩ = (–7, 5).

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

Corresponding sides are proportional

Corresponding angles change

Distances and angles are preserved

Only slopes are preserved

That is the defining property of translations.

Explanation

That is the defining property of translations.

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

⟨0, 9⟩

⟨0, –9⟩

⟨–9, 0⟩

⟨9, 0⟩

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

Explanation

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

Congruence Through Translations

1) Which transformation best demonstrates that two polygons are congruent?

2)

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

2) If A(0, 4) → A'(0, –3), which translation vector is correct?

3) Translations are considered what type of transformation?

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

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

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

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

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

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

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'?

11) Which statement is always true?

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

13) Why do translations prove congruence?

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

15) Which vector moves a point 9 units down?

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

17) Which of the following describes two congruent figures?

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

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

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