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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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What is the measure of [math]ang B'A'C'[/math], rounded to 1 decimal place?
  1. 63.4°
  2. 21.1°
  3. 88.3°
  4. 116.6°
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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What is the measure of [math]ang A'B'C'[/math], rounded to 1 decimal place?
  1. 104.0°
  2. 88.6°
  3. 25.3°
  4. 76.0°
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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What is the measure of [math]ang A'C'B'[/math], rounded to 1 decimal place?
  1. 82.1°
  2. 40.6°
  3. 13.5°
  4. 121.8°
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 [math]Delta ABC[/math] and the side lengths of the image [math]Delta A'B'C' ?[/math]
  1. [math](A'B')/(AB) = (B'C')/(BC) = (A'C')/(AC)[/math]
  2. [math]A'B' = 2AB, \ B'C' = 2BC, \ A'C' = 2AC[/math]
  3. [math]A'B' + B'C' + A'B' = 1/3(AB+ BC+ AC)[/math]
  4. [math]A'B'^2 = BC^2 + AC^2, \ B'C'^2 = AB^2 +AC^2, \ A'C'^2 = AB^2 + BC^2 [/math]
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2
The coordinates of the vertices of [math]Delta ABC[/math] are A(3,2), B(4,5), and C(1,1). The coordinates of the vertices of [math]Delta LMN[/math] are L(8,-2), M(10,4), and N(4,-4). Which of the following sequences of transformations, applied to [math]Delta ABC[/math], shows that [math]Delta ABC \ ~ \ Delta LMN ?[/math]
  1. A translation of 2 units right and 2 units down, and then a dilation of factor [math]3/2[/math] 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 [math]Delta ABC[/math] and the angle measures of the image, [math]Delta A'B'C' ?[/math]
  1. [math]m ang B'A'C' = m ang BAC^2 , \ m ang A'B'C' = m ang ABC ^2, \ m ang A'C'B' = m ang ACB ^2 [/math]
  2. [math]m ang BAC = 2m ang B'A'C', \ m ang ABC = 2m ang A'B'C', \ m ang ACB = 2m ang A'C'B'[/math]
  3. [math]m ang BAC = m ang B'A'C', \ m ang ABC = m ang A'B'C', \ m ang ACB = m ang A'C'B'[/math]
  4. [math]m ang BAC = 1/3 m ang B'A'C', \ m ang ABC = 1/3 m ang A'B'C', \ m ang ACB = 1/3 m ang A'C'B'[/math]
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2

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The previous questions have shown that [math]Delta ABC \ ~ \ Delta A'B'C'[/math]. 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).
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2
The coordinates of the vertices of [math]Delta FGH[/math] are [math]F(0,1)[/math], [math]G(3,-1)[/math], and [math]H(5,3)[/math]. The coordinates of the vertices of [math]Delta SRT[/math] are [math]S(0,-1)[/math], [math]R(3/2,0)[/math], and [math]T(5/2, -2)[/math]. Which of the following sequences of transformations, applied to [math]Delta FGH[/math], shows that [math]Delta FGH \ ~ \ Delta SRT ?[/math]
  1. A translation 2 units down, and then a dilation by a factor of [math]1/2[/math] centered at the origin.
  2. A rotation of 180° about the origin, and then a dilation by a factor of [math]1/2[/math] centered at the origin.
  3. A translation of a [math]1/2[/math] unit up, and then a dilation by a factor of [math]1/2[/math] centered at the origin.
  4. A translation of 1 unit up, a reflection over the x-axis, and then a dilation by a factor of [math]1/2[/math] centered at the origin.
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.2
If [math]Delta TUV \ ~ \ Delta T'U'V'[/math] and [math](TU)/(T'U') = 3/2[/math], determine the value of [math](U'V')/(UV)[/math].
  1. [math]9/4[/math]
  2. [math]3/2[/math]
  3. [math]2/3[/math]
  4. Not enough information.
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2
The coordinates of the vertices of [math]Delta CDE[/math] are C(-4,-4), D(-1,-1), and E(0,5). The coordinates of the vertices of [math]Delta JKL[/math] are J(-8,8), K(-2,2), and L(10,0). Which of the following sequence of transformations, applied to [math]Delta CDE[/math], shows that [math]Delta CDE \ ~ \ Delta JKL ?[/math]
  1. A rotation of 90° counterclockwise about the origin, and then a dilation of factor -2 centered at the origin.
  2. A reflection over the line [math]y=2[/math], and then a dilation of factor 2 centered at the origin.
  3. A translation of 2 units left and 4 units up, and then a dilation of factor 2 centered at the origin.
  4. A reflection over the line [math]y=x[/math], and then a dilation of factor [math]-2[/math] centered at the origin.
Grade 10 Symmetry and Transformations CCSS: HSG-SRT.A.2
[math]Delta EFG[/math] has vertices located at E(3,7), F(-1,4), and G(2,1). [math]Delta TUV[/math] has vertices located at T(-9,15), U(-1,9), and V(-7,3). Which of the following sequences of transformations, applied to [math]Delta EFG[/math], shows that [math]Delta EFG \ ~ \ Delta TUV ?[/math]
  1. A translation of 1 unit right and 1 unit up, a rotation of 90° counterclockwise about the origin, and then a dilation of factor 2 centered at the origin.
  2. A translation of 6 units right and 4 units down, a rotation of 90° about the origin, and then a dilation of factor 2 centered at (3,3).
  3. A translation of 1 unit right and 1 unit up, a reflection over the y-axis, and then a dilation of factor 2 centered at (1,1).
  4. A translation of 3 units left and 4 units up, and then a dilation of factor [math]3/2[/math] centered at the origin.
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