Quadrilaterals

Right angles in shapes (informal definition)

CCSS Math: 3.G.A.1
Identify right angles in shapes.

Introduction

Many shapes have corners. We call a corner a right angle if we can fit a little square perfectly inside it.

Consider the trapezoid

Let's draw a square in each corner.
In which corners did the little square fit perfectly?
The trapezoid has two right angles.

Practice

First, let's study some more examples.
Now, try it yourself.
How many right angles are in this square?
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

How many right angles are in this pentagon?
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

[Show solutions.]
The square has four right angles.
The pentagon has two right angles.

Challenge problem

How many right angles does this shape have?
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

[Help, I'm stuck.]
Squares fit perfectly in two of the corners, so there are two right angles.