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Tenth Grade (Grade 10) Geometry and Measurement Questions

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Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.4
Ellen is given four points and their coordinates: A(-2,0);B(4,4);C(7,3);D(1,-1). She is asked to show whether these points form a parallelogram. In order to do so, she finds the midpoints of ¯AC and ¯BD. She finds they are both (52,32). She reasons that, since the midpoints of ¯AC and ¯BD (the diagonals of the quadrilateral) are coincident, these line segments intersect at each other's midpoints and thus bisect each other. Therefore, she concludes that ABCD is a parallelogram. Is she correct, and why?
  1. No, she made a calculation error, and the midpoints of ¯AC and ¯BD are not the same.
  2. No, she must show that both sets of opposite sides are parallel.
  3. No, her reasoning is incorrect. She must find the equations of lines ↔AC and ↔BD, find their intersection point, P, and then see if ¯AP,¯PC are congruent, and then if ¯BP,¯DP are congruent.
  4. Yes, this sufficiently shows that ABCD is a parallelogram.
Grade 10 Angles
What is the term for a pair of angles that add up to 180 degrees?
  1. vertical angles
  2. complementary angles
  3. supplementary angles
  4. adjacent angles
Grade 10 Points, Lines, and Planes CCSS: HSG-CO.A.1
                is the set of two points A and B and all the points in between.
  1. Opposite rays
  2. Ray
  3. Line
  4. Half-line
  5. Segment
Grade 10 Metric System and SI
The SI unit of volume is the
  1. kilogram.
  2. meter.
  3. liter.
  4. hectare.
Grade 10 Symmetry and Transformations CCSS: HSG-CO.B.7
Which of the following transformations would show if ΔABD≅ΔCDB?
Parallelogram ABCD v3
  1. Translate triangle ABD right by the length of ¯AD.
  2. Reflect triangle ABD over the line containing ¯BD.
  3. Rotate triangle ABD 180° about the midpoint of ¯BD.
  4. Reflect triangle ABD over the line containing ¯BD then translate 14→BD.
Grade 10 Angles
A ray that divides an angle into two congruent angles.
  1. transversal
  2. collinear
  3. angle bisector
  4. parallel
Grade 10 Metric System and SI
The measurement system that most scientists use.
  1. Inches
  2. Millimeters
  3. Meters
  4. Metric
Grade 10 Points, Lines, and Planes
Using the distance formula, find the distance between the two points A (4,7) and B (3,-2).
  1. 7
  2. √19
  3. √20
  4. √82
Grade 10 Coordinate Geometry CCSS: HSG-GPE.B.6
If a segment has one endpoint at (9, 8) and a midpoint at (0, 9), what are the coordinates of the other endpoint?
  1. (-9,10)
  2. (112,-1)
  3. (412,-12)
  4. (812,412)
Grade 10 Points, Lines, and Planes
The union of three noncollinear points and the line segments connecting them.
  1. triangle
  2. angle
  3. diagonal
  4. bisector
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.2
Are these two triangles are similar?
Triangle 1: A = 125, C = 18
Triangle 2: B = 125, C = 35
Acute Triangle ABC v1Acute Triangle ABC v2
  1. Yes, the triangles are similar.
  2. No, the triangles are not similar.
Grade 10 Similar and Congruent Figures CCSS: HSG-SRT.A.3
ΔEFG is an obtuse isosceles triangle, m∠E=39°, and ¯EG is the longest side. ΔJKL is also an obtuse isosceles triangle and m∠L=102°. Which of the following is correct?
  1. ΔEFG ~ ΔJKL
  2. ΔEFG ~ ΔJLK
  3. These two triangles are not similar.
  4. These two triangles may or may not be similar, but there is not enough information to be certain.
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