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Tenth Grade (Grade 10) Two Dimensional Shapes Questions

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Grade 10 Triangles CCSS: HSG-CO.B.7
You are given two triangles, ABC and FGH. There is a sequence of translations and reflections that map triangle ABC to triangle FGH, such that ¯AB maps to ¯GH and ¯AC maps to ¯GF. Which of the following statements is correct?
  1. There is not enough information to say if the triangles are congruent.
  2. ΔABC≅ΔHGF
  3. ΔABC≅FHG
  4. ΔABC≅ΔGHF
Grade 10 Circles CCSS: HSG-MG.A.2
A piece of land, in the shape of a circle with a diameter of 10 ft, has about 15 worms on it right now. What is the density of worms on this circle of land, rounded to two decimal places?
  1. 0.05 worms per square foot
  2. 0.19 worms per square foot
  3. 1.50 worms per square foot
  4. 1178.10 worms per square foot
Grade 10 Circles CCSS: HSG-C.A.1

This question is a part of a group with common instructions. View group »

If circle B's radius is larger that circle A's radius, what must change in our work to show that the two circles are similar?
  1. Nothing needs to change.
  2. They cannot be similar in this case.
  3. Circle A must be translated to circle B.
  4. The dilation scale factor must change.
Grade 10 Circles CCSS: HSG-C.A.1

This question is a part of a group with common instructions. View group »

After increasing the radius of circle B, such that it is equal to the radius of circle A, how can we be sure that the two circles will lie exactly on top of each other?
  1. Since a circle is defined as a set of points a certain distance from a center, all the points on circle B will now be the same distance away from A as the points on circle A.
  2. Because a dilation is a rigid transformation, all the points on circle B must move by the same amount.
  3. Since the centers of the two circles are coincident, the rest of the circle must also be coincident.
  4. We can't be sure and need to use more radii from each circle to show this.
Grade 10 Two Dimensional Shapes
Which is always a regular polygon?
  1. pentagon
  2. hexagon
  3. square
  4. triangle
  5. rhombus
Grade 10 Triangles
In triangle ABC, side a is 13.2, side b is 12.8 and side c is 14.3. Which angle will be the largest?
  1. Angle A
  2. Angle B
  3. Angle C
  4. Answer cannot be determined
Grade 10 Quadrilaterals
Which of the following is a valid conclusion?
  1. All rhombi are squares.
  2. All rhombi are rectangles.
  3. All quadrilaterals are parallelograms.
  4. All rectangles are parallelograms.
Grade 10 Triangles CCSS: HSG-CO.C.10

This question is a part of a group with common instructions. View group »

What is the missing reason in step 8?
  1. Corresponding angles of congruent triangles are congruent
  2. Corresponding angles of similar triangles are congruent
  3. AAA
  4. Definition of congruent angles
Grade 10 Circles
If 2 circles have congruent radii, then the 2 circles are                      .
  1. congruent circles
  2. concentric circles
  3. intersecting circles
  4. circumscribed circles
Grade 10 Circles

This question is a part of a group with common instructions. View group »

Given the work in steps B - H to show that two circles are similar, could we use this to show that any two spheres are similar? If so, what needs to be changed or added?
  1. No, this is not possible.
  2. Yes, by starting with spheres, and projecting them onto the xy-plane, we can then follow the steps already established.
  3. Yes, but we would need to perform completely different transformations since we are now working in three dimensions.
  4. Yes, start with spheres instead of circles and then follow nearly identical steps.
Grade 10 Circles
In the circle, which line segment is a secant?
Circle with Secant CD and Tangent AB
  1. ¯AB
  2. ¯BC
  3. ¯BD
  4. ¯CD
Grade 10 Circles

This question is a part of a group with common instructions. View group »

Not only are all circles similar, but all spheres are similar as well. Are these two facts related? Why or why not?
  1. No, it is just chance.
  2. No, a circle is two dimensional and a sphere is three dimensional.
  3. Yes, the reason being that both for circles and spheres, their shape is always the same and their size depends on the radius.
  4. Yes, the reason being that both are not polygons.
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