Triangle Similarity: AA Answers

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1
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Read the proof.Given: AB ∥ DEProve: △ABC ~ △EDC

Question illustration
A
AA similarity theorem
B
ASA similarity theorem
C
AAS similarity theorem
D
SAS similarity theorem
2
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ΔXYZ was reflected over a vertical line, then dilated by a scale factor of , resulting in ΔX'Y'Z'. Which must be true of the two triangles? Select three options.

Question illustration
A
△XYZ ~ △X'Y'Z'
B
XZY ≅ Y'Z'X'
Option B
C
YX ≅ Y'X'
D
XZ = 2X'Z'
E
mYXZ = 2mY'X'Z'
Option E
4

Two similar triangles are shown.

Question illustration
A
rotated
B
reflected
C
translated
D
dilated
5

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.

Question illustration
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.
6

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
7

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
8

Which diagram could be used to prove △ABC ~ △DEC using similarity transformations?

A
Triangle A B C is reflected across side A C and then is dilated to form smaller triangle D C E.
Option A
B
Triangle A B C is reflected, translated to the left, and then is dilated to form triangle D C E.
Option B
C
Triangles A B C and D E C are shown. The angle measures differ between the 2 triangles.
Option C
D
Triangles A B C and D E C are connected at point C. The triangles are shaped differently.
Option D
9

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

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