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Common Core Standard HSG-SRT.A.2 Questions

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

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Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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What is the length of side ¯AB?
  1. 92 units
  2. 310 units
  3. 9 units
  4. 97 units
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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What is the length of side ¯BC?
  1. 337 units
  2. 310 units
  3. 313 units
  4. 334 units
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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What is the length of side ¯AC?
  1. 373 units
  2. 282 units
  3. 610 units
  4. 122 units
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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Which of the following correctly states the relationship between the side lengths of the pre-image ΔABC and the side lengths of the image ΔABC?
  1. ABAB=BCBC=ACAC
  2. AB=2AB, BC=2BC, AC=2AC
  3. AB+BC+AB=13(AB+BC+AC)
  4. AB2=BC2+AC2, BC2=AB2+AC2, AC2=AB2+BC2
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2
The coordinates of the vertices of ΔABC are A(3,2), B(4,5), and C(1,1). The coordinates of the vertices of ΔLMN are L(8,-2), M(10,4), and N(4,-4). Which of the following sequences of transformations, applied to ΔABC, shows that ΔABC ~ ΔLMN?
  1. A translation of 2 units right and 2 units down, and then a dilation of factor 32 centered at the origin.
  2. A translation of 2 units right, a reflection over the x-axis, and then a dilation of factor 3 centered at the origin.
  3. A translation of 1 unit right and 3 units down, and then a dilation of factor 2 centered at the origin.
  4. A translation of 3 units left and 1 unit up, and then a dilation of factor -2 centered at the origin.
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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Which of the following correctly states the relationship between the angle measures of the pre-image ΔABC and the angle measures of the image, ΔABC?
  1. mBAC=mBAC2, mABC=mABC2, mACB=mACB2
  2. mBAC=2mBAC, mABC=2mABC, mACB=2mACB
  3. mBAC=mBAC, mABC=mABC, mACB=mACB
  4. mBAC=13mBAC, mABC=13mABC, mACB=13mACB
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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The previous questions have shown that ΔABC ~ ΔABC. If additional transformations were added to the sequence of transformations in question 1, (transformations such as another translation, a rotation, another reflection, or another dilation), would this alter the results in the previous two questions?
  1. The results in the previous two questions would only be altered if another dilation were added to the sequence of transformations. Otherwise, there would be no change.
  2. Adding any one of the additional transformations would affect the results in the previous two questions.
  3. None of the additional transformations, if added to the sequence of transformations, would affect the results in the previous two questions.
  4. Adding additional transformations would only affect the results in the previous two questions if they included a transformation not around the origin (such as a rotation about a point that is not the origin, or a dilation not centered at the origin).
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