Section A Practice Problems

Problem 1

Here are 6 shapes:

6 shapes.
6 shapes. A. 3 equal sides and angles. B. 3 sides of different length, one right angle. C. 4 sides, opposite sides parallel and equal length, 4 right angles. D. 4 equal sides, opposite sides parallel, opposite angles equal size. E. 4 equal sides. all right angles. F. 4 sides, opposite sides parallel and equal length, , opposite angles equal size, 2 acute angles, 2 obtuse angles.

  1. Which shapes are quadrilaterals?
  2. Which shapes are rhombuses?
  3. Which shapes are rectangles?
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Solution
  1. C, D, E, F
  2. D, E
  3. C, E

Problem 2

Find the perimeter and area of the rectangle. Explain or show your reasoning.

rectangle, length, 13. Width, 6.

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Solution

The perimeter is 38 units. The area is 78 square units. Sample response: 13+6=1913 + 6 = 19 and 19+19=3819 + 19 = 38. The area is 78 because 13×6=7813 \times 6 = 78.

Problem 3

Select all images that show half of the rectangle shaded.

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Solution
B,C,E

Problem 4

Here are 4 shapes:

4 shapes. All have 4 sides.
4 shapes. All have 4 sides. A. 1 pair of parallel sides. B. 2 pair of opposite parallel sides with equal length. C. 2 pair of opposite parallel sides. all 4 sides are equal length. D. 2 pairs of opposite parallel sides with equal length. 4 right angles.

  1. Name some attributes that all the shapes share.
  2. Name some attributes that the shapes do not share.
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Solution

Sample responses:

  1. They are all quadrilaterals. They all have at least two sides that are equal. They all have at least one set of parallel sides. They all have at least two angles that are equal.
  2. Some of the shapes have all equal sides. Some of the shapes have all equal angles. Some of the shapes have two pairs of parallel sides.

Problem 5

Here are 4 triangles:

4 triangles, all have 3 sides of different length. A. 1 obtuse angle, 2 acute angles. B. 3 acute angles. C and D. 1 right angle, 2 acute angles.

  1. Which triangles are right triangles?
  2. Which triangles have an obtuse angle?
  3. Which triangles have 3 acute angles?
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Solution
  1. C and D
  2. A
  3. B

Problem 6

Here are 3 rhombuses:

3 rhombuses. all have opposite sides parallel and same length, opposite angles equal size. A, B, 2 acute, 2 obtuse angles. C, 4 right angles.
  1. What attributes do the 3 rhombuses share?
  2. What attributes are different in the 3 rhombuses?
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Solution

Sample response:

  1. The four sides are the same length in each shape. The opposite angles have the same measure.
  2. The angles are different. Two of the shapes have a pair of obtuse and a pair of acute angles and the other has all right angles.

Problem 7

Draw any lines of symmetry for these letters:

6 figures with the shapes of the capital letters, A, C, G, N, O, Z.

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Solution

Sample responses: Letter A has a vertical line of symmetry. C has a horizontal line of symmetry. O has an infinite number of lines of symmetry, any line that goes through the center of the O. G, N, and Z have none.

Problem 8

Complete each figure so that the dashed line is a line of symmetry for the completed figure.

triangle on grid. The horizontal side overlaps a dashed line of symmetry.

parallelogram, right side overlapping a dashed line.

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Solution

Sample response:

grid solution

symmetry solution

Problem 9

Draw all the lines of symmetry you can find in this snowflake. How many can you find?

drawing of a snowflake with 6 equal parts. symmetric down the middle with 3 petals on each side.

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Solution

Sample response: There are 6 lines of symmetry, 3 that go through opposite “points” on the snowflake and 3 that go through the spaces between the “leaves” or “petals.”

Problem 10

Draw each shape and all the lines of symmetry you can find in it.

  • Rectangle
  • Rhombus
  • Square
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Solution

Sample responses:

  • Rectangle showing 2 lines of symmetry through the middle of opposite sides
  • Rhombus showing 2 lines of symmetry through opposite vertices
  • Square with 4 lines of symmetry:, 2 going through opposite vertices, 2 going through the middle of opposite sides