Unit 8 Family Materials

Properties of Two-dimensional Shapes

Properties of Two-dimensional Shapes

In this unit, students classify triangles and quadrilaterals based on the attributes of their sides and angles. They also learn about lines of symmetry in two-dimensional figures. Students then use these attributes of figures to solve geometric problems, including those about perimeter and area. 

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

In this section, students think about different attributes of two-dimensional shapes, such as: 

  • number of sides
  • length of sides
  • size of angles
  • presence of parallel or perpendicular lines
  • symmetry 

They examine shapes, classify them by the attributes they share, and explain their classifications. For example, given examples of parallelograms and rhombuses, students think about what must be true about the sides and angles of each type of quadrilaterals.

Quadrilaterals N, U, and Z are parallelograms.

Quadrilaterals. N. U. Z.

Quadrilaterals AA, EE, and JJ are rhombuses.

Quadrilaterals. A, A. E, E. J, J.

Students also learn about symmetry—whether a figure can be folded along a line into two equal halves that match up exactly. They draw lines of symmetry for given figures, and complete drawings of figures that are halved by a line of symmetry.

symmetric shapes


Section B: Reason About Properties to Solve Problems

In this section, students reason about measurements in shapes.

Students begin by finding the perimeter of shapes where the side lengths are all given. Then, they look at shapes where the side lengths are not all given but can be found because of the attributes of the shapes (for example, the opposite sides are the same length) or because the perimeter is known. 

Figures P, Q, and R each have 1 line of symmetry.
Figure Q has 4 lines of symmetry. All figures have a perimeter of 64 inches.

Figures. P. Q. R. S

As they find perimeters and side lengths, students also practice performing operations on whole numbers and fractions.

Try it at home!

Near the end of the unit, ask your student to solve the following problems:

  • What attributes do these figures all have in common? For each figure, how many lines of symmetry can you find?
5 shapes. From left to right. square. parallelogram. Pentagon with 5 equal side lengths. rectangle. triangle with 2 equal side lengths.
  • What shapes do you see around the home or in places we visit? How could we classify them into categories?

Questions that may be helpful as they work:

  • Can you describe the attributes of these shapes?
  • What does it mean to have a line of symmetry?