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Tenth Grade (Grade 10) Geometry and Measurement Questions

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Grade 10 Pythagorean Theorem and Applications
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.7
Which of the following transformations would show if [math]Delta ABC ~= Delta ADC ?[/math]
Diamond ABCD
  1. Translate triangle ABC down by vertical distance between [math]bar{AC}[/math] and point B.
  2. Reflect triangle ABC over the line containing [math]bar{AC}[/math].
  3. Rotate triangle ABC 180° around midpoint of [math]bar{AC}[/math].
  4. Translate triangle ABC down by half the vertical length between [math]bar{AC}[/math] and point B, and then rotate it 180° about its centroid.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8
You are given two triangles, ABC and DEF. If you know that [math]bar{AB}~=bar{DE}, bar{BC}~=bar{EF}[/math] and [math]ang B ~= ang E[/math]. Which of the following could be true? Select all that apply.
  1. There is not enough information to make any conclusions.
  2. A dilation and translation map triangle ABC onto triangle DEF.
  3. A translation and rotation map triangle ABC onto triangle DEF.
  4. A rotation and reflection map triangle ABC onto triangle DEF.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.A.2
How is the transformation between the two graphs best described?
Graph - Linear Function y=1/2x Graph - Linear Function y=2x
  1. translation
  2. rotation
  3. reflection
  4. reflection and rotation
Grade 10 Triangles
What is the definition of complimentary angles?
  1. Two angles that add to be [math]180 deg[/math]
  2. Two angles that have a difference of [math]90 deg[/math]
  3. Two angles add to be [math]90 deg[/math]
  4. Two angles that have a difference of [math]180 deg[/math]
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.7
In the regular hexagon pictured, the center is M (not pictured). Which of the following transformations show that [math]Delta BMC ~= Delta DME ?[/math] Choose all correct answers.
Hexagon ABCDEF
  1. Reflect triangle BMC over the line joining the midpoints of [math]bar{CD}[/math] and [math]bar{AF}[/math].
  2. Rotate triangle BMC 120° counterclockwise about point M.
  3. Translate triangle BMC right the length of [math]bar{CD}[/math], then rotate it 120° clockwise about its centroid.
  4. Rotate triangle BMC 60° clockwise about point M, then reflect it over the line passing through C and F.
Grade 10 Angles
Which of these is not a type of angle?
  1. acute
  2. obtuse
  3. skew
  4. right
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.8
You are given two triangles, ABC and GHF, plotted on a set of axes. You know that you can map [math]bar{AB}[/math] onto [math]bar{GH}[/math] by a reflection over the x-axis and a rotation of 160° clockwise about the origin. You also know that [math]ang A ~= ang G[/math] and [math]ang B ~= ang H[/math]. Which of the following statements are true? There may be more than one correct answer.
  1. [math]Delta ABC ~= Delta GHF[/math]
  2. [math]bar{BC}[/math] can be mapped onto [math]bar{HF}[/math] by a reflection over the x-axis and a rotation of 160° clockwise about the origin.
  3. [math]bar{AC}[/math] can be mapped onto [math]bar{GF}[/math] by a reflection over the x-axis and a rotation of 160° clockwise about the origin.
  4. [math]m ang C = m ang F + 160°[/math]
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.7
Which of the following transformations would show if [math]Delta ABD ~= Delta CDB ?[/math]
Parallelogram ABCD v3
  1. Translate triangle ABD right by length of [math]bar{AD}[/math].
  2. Reflect triangle ABD over the line containing [math]bar{BD}[/math].
  3. Rotate triangle ABD 180° about the midpoint of [math]bar{BD}[/math].
  4. Reflect triangle ABD over the line containing [math]bar{BD}[/math] then translate [math]1/4 vec{BD}[/math].
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.7
Which of the following transformations would show if [math]Delta ABF ~= Delta ECD ?[/math]
Trapezoid ABCDEF
  1. Translate triangle ABF right by the length of [math]bar{FD}[/math].
  2. Reflect triangle ABF about the line joining the midpoints of [math]bar{BC}[/math] and [math]bar{FD}[/math].
  3. Rotate triangle ABF 180° about the midpoint of the line joining the midpoints of [math]bar{BC}[/math] and [math]bar{FD}[/math].
  4. Translate triangle ABF right by the length of [math]bar{FE}[/math].
Grade 10 Similar and Congruent Figures
A triangle where [math]ang B = 30°[/math] will be similar to a triangle where [math]ang C = 60°.[/math]
Right Triangle ABC v1
  1. Always
  2. If the side lengths are the same
  3. If they are right triangles
  4. Never
Grade 10 Angles
An angle that measures exactly 90 degrees.
  1. acute
  2. obtuse
  3. straight
  4. complementary
  5. none of the above
Grade 10 Points, Lines, and Planes
Points contained on the same line.
  1. coplanar
  2. collinear
  3. line
  4. plane
Grade 10 Angles
An angle that measures between 0 and 90 degrees.
  1. acute
  2. complementary
  3. right
  4. straight
  5. none of the above
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