Proving Similarity with Transformations

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Thames
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| Questions: 20 | Updated: Nov 24, 2025
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1) Which sequence proves two right triangles are similar?

Explanation

Dilation changes size while keeping shape, translation slides. Together they prove similarity.

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About This Quiz
Proving Similarity With Transformations - Quiz

Let's put it all together to make solid similarity proofs! In this quiz, you’ll use clear steps—like dilation then a slide/turn/flip—to send one figure onto a similar copy. You’ll write simple rules, track coordinates, and explain why angles match and sides scale by the same factor. By the end, you’ll... see moreprove similarity with clean, confident reasoning.
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2)
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2) A triangle with vertices (1,1), (2,3), (3,1) is translated 4 units right. One new vertex is:

Explanation

Translate 4 units right: add 4 to x. (1,1) → (5,1).

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3) Point P is located at (–3, 4). A 90° clockwise rotation about the origin sends P to:

Explanation

90° clockwise about origin: (x, y) → (y, –x). (–3,4) → (4,3).

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4) A dilation with center (0,0) and scale factor ½ maps (6, –8) to:

Explanation

Scale by 1/2 about origin: (6, –8) → (3, –4).

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5) The preimage has side lengths 5, 6, and 7. The image has 10, 12, and 14. The transformation is:

Explanation

All sides doubled: 5→10, 6→12, 7→14.

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6) Triangle A is located at (0,0), (1,0), (0,1). Triangle B is located at (0,0), (2,0), (0,2). Which transformation maps A onto B?

Explanation

Coordinates double: (0,0),(1,0),(0,1) → (0,0),(2,0),(0,2).

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7) Which similarity transformation could map a rectangle to another rectangle with doubled side lengths?

Explanation

Doubling side lengths is a scale change.

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8) A rotation of 270° counterclockwise is equivalent to:

Explanation

270° counterclockwise = 90° clockwise.

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9) A reflection across the x-axis preserves:

Explanation

Reflections preserve lengths and angles but reverse orientation.

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10) A sequence of a reflection and a translation will always result in figures that are:

Explanation

Reflection and translation are isometries, so distance and angles are preserved.

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11) A pentagon is dilated by a scale factor of 4. Which statement is correct about the image?

Explanation

Dilations keep angles; lengths and perimeter scale.

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12) Which is an example of two figures that are similar but not congruent?

Explanation

Sides are proportional (scale factor 2), so similar but not congruent.

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13) A triangle is rotated 90° counterclockwise and then translated 3 units up. The resulting triangle is:

Explanation

Rotation + translation are isometries; size and shape unchanged.

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14) Which is true of similarity transformations?

Explanation

Similarity transformations keep angles and side ratios.

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15) A trapezoid has bases 6 and 10. A second trapezoid has bases 9 and 15, and their corresponding angles match. What does this prove about the trapezoids?

Explanation

Bases are in the same ratio 6:10 = 9:15 and angles correspond.

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16) Which transformation does NOT change orientation?

Explanation

Translations do not change orientation. (Reflections reverse it; rotations and positive dilations preserve it.)

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17) Which sequence maps a figure onto a congruent figure?

Explanation

Both are rigid motions, so the image is congruent to the original.

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18) Point A is located at (2, –1). After reflection across the y-axis, A is mapped to:

Explanation

Reflect across y-axis: (x, y) → (–x, y).

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19) Which transformation always preserves distance?

Explanation

Translations preserve all distances and angles.

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20) Which set of transformations could map a triangle onto a similar triangle?

Explanation

Dilation creates a similar figure; translation repositions it.

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Which sequence proves two right triangles are similar?
A triangle with vertices (1,1), (2,3), (3,1) is translated 4 units...
Point P is located at (–3, 4). A 90° clockwise rotation about the...
A dilation with center (0,0) and scale factor ½ maps (6, –8) to:
The preimage has side lengths 5, 6, and 7. The image has 10, 12, and...
Triangle A is located at (0,0), (1,0), (0,1). Triangle B is located at...
Which similarity transformation could map a rectangle to another...
A rotation of 270° counterclockwise is equivalent to:
A reflection across the x-axis preserves:
A sequence of a reflection and a translation will always result in...
A pentagon is dilated by a scale factor of 4. Which statement is...
Which is an example of two figures that are similar but not congruent?
A triangle is rotated 90° counterclockwise and then translated 3...
Which is true of similarity transformations?
A trapezoid has bases 6 and 10. A second trapezoid has bases 9 and 15,...
Which transformation does NOT change orientation?
Which sequence maps a figure onto a congruent figure?
Point A is located at (2, –1). After reflection across the y-axis, A...
Which transformation always preserves distance?
Which set of transformations could map a triangle onto a similar...
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