Triangle Similarity: AA Answers

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1
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Triangle A B C is reflected across side A C and then is dilated to form smaller triangle D C E. Angles B C A and D C E are right angles.

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A
The triangles are not similar because only one pair of corresponding angles is congruent.
B
The triangles are similar because all right triangles can be mapped to each other using a series of transformations.
C
The triangles are not similar because they share a common segment and vertex.
D
The triangles are similar because all pairs of corresponding angles are congruent.
2
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On a coordinate plane, triangle A B C has points (negative 9, 3), (negative 9, 6), (0, 3) and triangle A double-prime B double-prime C double-prime has points (3, negative 1), (3, negative 2), and (0, negative 1).

Question illustration
A
a reflection over the x-axis, then a dilation by a scale factor of 3
B
a reflection over the x-axis, then a dilation by a scale factor of
Option B
C
a 180° rotation about the origin, then a dilation by a scale factor of 3
D
a 180° rotation about the origin, then a dilation by a scale factor of
Option D
3

Two similar triangles are shown.

Question illustration
A
rotated
B
reflected
C
translated
D
dilated
4

The composition is applied to △RST to create the image of △R"S"T", which is not shown.

Question illustration
A
(negative three-halves, nine-halves)
Option A
B
(negative nine-halves, fifteen-halves)
Option B
C
(nine-halves, negative three-halves)
Option C
D
(negative fifteen-halves, 0)
Option D
6

Triangle A E C is shown. Line segment B D is drawn near point C to form triangle B D C.

Question illustration
A
∠BDC and ∠AED are right angles
B
AE ≅ ED
C
△BDC is a right triangle
D
∠DBC ≅ ∠DCB
7

Which composition of transformations will create a pair of similar, not congruent triangles?

A
a rotation, then a reflection
B
a translation, then a rotation
C
a reflection, then a translation
D
a rotation, then a dilation
9

Two similar triangles are shown.

Question illustration
A
rotated
B
reflected
C
translated
D
dilated
10

Triangle A B C is reflected and then dilated to form smaller triangle A double-prime B double-prime C double-prime

Question illustration
A
a rotation and a dilation
B
a rotation and a reflection
C
a reflection and a dilation
D
a translation and a dilation

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