Section B: Practice Problems The Hierarchy of Shapes

Section Summary

Details

In this section we sorted and analyzed different kinds of quadrilaterals and triangles. We described their properties. For example:

A rectangle is a quadrilateral with 4 right angles.
A rhombus is a quadrilateral with 4 equal sides.
A square is a quadrilateral with 4 right angles and 4 equal sides.

We also described how the shapes are related to each other. For example, we can see that a square is always a rhombus because it has the properties of a rhombus. A square is also always a rectangle because it has the properties of a rectangle. On the other hand, a rectangle does not need to be a square because its side lengths don’t have to all be the same. And a rhombus does not need to be a square because its angles do not have to be right angles.

Problem 1 (Lesson 4)

Determine whether the statement is true or false. Explain or show your reasoning.

Quadrilateral on grid. all sides equal length. no right angles.

The shape is a rectangle.
The shape is a square.
The shape is a rhombus.

Problem 2 (Lesson 5)

Draw a trapezoid that is also a parallelogram. Explain how you know it is a trapezoid and a parallelogram.
Draw a trapezoid that is not a parallelogram. Explain how you know it is a trapezoid but is not a parallelogram.

Problem 3 (Lesson 6)

Determine if you can make each given shape so that it contains these two sides. Explain your reasoning.

a square

a rectangle

a rhombus

2 line segments of equal length on grid. do not meet at a right angle.

Problem 4 (Lesson 7)

Decide if each statement is true or false. Explain or show your reasoning.

A parallelogram is sometimes a rhombus.
A rhombus is always a parallelogram.
A trapezoid is never a rectangle.
A rectangle is never a square.
A parallelogram is always a trapezoid.

Problem 5 (Lesson 8)

For each description, draw a right triangle with the described side lengths on the grid or explain why there is no such right triangle.

2 equal side lengths

3 equal side lengths

3 different side lengths

Problem 6 (Exploration)

Jada cut a quadrilateral in half, from one vertex to the opposite vertex, and she got two isosceles triangles. What kind of quadrilateral could Jada have cut in half? Explain or show your reasoning.
Elena put together two right triangles to make a quadrilateral. What kind of quadrilateral could Elena have made? Explain or show your reasoning.

Problem 7 (Exploration)

Can you find a square on the grid that does not have a vertical or horizontal side? Explain or show your reasoning.
Draw the line segment from $(4, 4)$ to $(6, 5)$ . Can you find a square that contains this segment as one of its sides?