Section A: Practice Problems Side Lengths, Angles, and Lines of Symmetry

Section Summary

Details

In this section, we looked at different attributes of shapes, such as the number and length of sides, the measurements of sides and angles, and whether the shapes had parallel and perpendicular sides.

We then used these attributes to classify quadrilaterals and triangles.

Triangles with a right angle are right triangles.

2 right triangles. Left one, all sides different length. Right one, 2 sides same length.

Quadrilaterals with two pairs of parallel sides are parallelograms.

2 parallelograms. both with opposite sides parallel and equal length.

Quadrilaterals with two pairs of parallel sides and four right angles are rectangles.

2 rectangles. Both with opposite sides parallel and equal length. Both with 4 right angles. 1 tilted, 1 not tilted.

Quadrilaterals with four equal sides are rhombuses.

2 rhombuses. Both with opposite sides parallel and all 4 sides equal length. 1 tilted, 1 not tilted.

Quadrilaterals with four equal sides and four right angles are squares.

2 squares. both with opposite sides parallel and all 4 sides of same length. Both with 4 right angles. one tilted, one not.

We also learned about lines of symmetry. A figure that has a line of symmetry can be folded along that line to create two halves that match up exactly.

symmetric shapes

Problem 1 (Pre-Unit)

6 shapes.

  1. Which shapes are quadrilaterals?

  2. Which shapes are rhombuses?

  3. Which shapes are rectangles?

Problem 2 (Pre-Unit)

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

rectangle, length, 13. Width, 6.

Problem 3 (Pre-Unit)

Select all images that show half of the shaded rectangle.

  1. rectangle completely shaded
  2. rectangle partitioned into two equal parts by vertical line with one part shaded
  3. rectangle partitioned into two equal parts by horizontal line with one part shaded
  4. rectangle partitioned into two parts by vertical line with the larger part shaded
  5. rectangle partitioned into two equal parts by diagonal line with one part shaded

Problem 4 (Lesson 1)

4 shapes. All have 4 sides.

  1. Name some attributes that these shapes share.

  2. Name some attributes that the shapes do not share.

Problem 5 (Lesson 2)

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 of the triangles are right triangles?

  2. Which of the triangles have an obtuse angle?

  3. Which of the triangles have 3 acute angles?

Problem 6 (Lesson 3)

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 rhombuses share?

  2. What attributes are different in the three rhombuses?

Problem 7 (Lesson 4)

Draw the lines of symmetry for these letters:

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

Problem 8 (Exploration)

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

  1. triangle on grid. The horizontal side overlaps a dashed line of symmetry.
  2. parallelogram, right side overlapping a dashed line.

Problem 9 (Exploration)

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

  1. triangle on grid. The horizontal side overlaps a dashed line of symmetry.
  2. parallelogram, right side overlapping a dashed line.

Problem 10 (Exploration)

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.

Problem 11 (Exploration)

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

  1. rectangle

  2. rhombus

  3. square