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Geometry (all content)

Course: Geometry (all content) > Unit 5

Lesson 1: Quadrilateral types
Math
Geometry (all content)
Quadrilaterals
Quadrilateral types
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Right angles in shapes (informal definition)

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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

A trapezoid. The direction of each side is as follows, beginning at the top and continuing in a clockwise pattern: straight line to the right, straight line down and left, straight line to the left, straight line up.
Let's draw a square in each corner.
A trapezoid with a square in each corner. The direction of each side is as follows, beginning at the top and continuing in a clockwise pattern: straight line to the right, straight line down and left, straight line to the left, straight line up.
In which corners did the little square fit perfectly?
A trapezoid with a square in each corner. There are 2 green squares in the upper and lower left corners. There are 2 red squares in the upper and lower right corners. Each green square is labeled right angle and each red square is labeled not a right angle. The direction of each side is as follows, beginning at the top and continuing in a clockwise pattern: straight line to the right, straight line down and left, straight line to the left, straight line up.
The trapezoid has two right angles.

Practice

First, let's study some more examples.
A rectangle with a square in each corner. The direction of each side is as follows, beginning at the top and continuing in a clockwise pattern: straight line to the right, straight line down, straight line to the left, straight line up.
A quadrilateral with a square in one corner. The direction of each side is as follows, beginning at the top and continuing in a clockwise pattern: straight line down and right, straight line down and left, straight line up and left, straight line up and right.
A right triangle with a square in one corner. The direction of each side is as follows, beginning at the top and continuing in a clockwise pattern: straight line to the right, straight line down and left, straight line up.
Now, try it yourself.
How many right angles are in this square?
A square shape with 4 sides. The direction of each side is as follows, beginning at the top and continuing in a clockwise pattern: straight line to the right, straight line down, straight line to the left, straight line up.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

How many right angles are in this pentagon?
A pentagon shape with 5 sides. The direction of each side is as follows, beginning at the top and continuing in a clockwise pattern: straight line to the right, straight line down and right, straight line down and left, straight line to the left, straight line up.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Challenge problem

How many right angles does this shape have?
A shape with 9 sides. The direction of each side is as follows, beginning at the top and continuing in a clockwise pattern: straight line to the right, straight line down and right, straight line to the right, straight line down and left, straight line down and right, straight line down and left, straight line to the left, straight line up, straight line up and right.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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