Plane Figures

I. Quadrilaterals Introduction

A quadrilateral is a polygon with four sides. The word ‘quadrilateral’ is derived from the Latin words ‘quadri,’ which means four, and ‘latus’, which means side.

A. Trapezoid 

A Trapezoid (Trapezium) is a type of quadrilateral where:

-one pair of opposite sides are parallel. 

B. Kite

A Kite is a type of quadrilateral that has:

-two pairs of consecutive equal sides 

-perpendicular diagonals

C. Parallelogram

A Parallelogram is a type of quadrilateral where:

-all opposite sides are parallel.

 

Types of parallelograms:

1. Rectangles

What makes a shape a rectangle?
-There are four right angles.

Here are some examples of rectangles:

2. Rhombuses
What makes a shape a rhombus?
-All sides are the same length.
-There are four sides because it is a quadrilateral.

Here are some examples of rhombuses:

3. Squares
What makes a shape a square?
-All sides are of equal length.
-There are four right angles.

Here are some examples of squares:

Note: A square is also is a type of rectangle and rhombus

II. Classifying Triangles

Angle Sum Property 

The angle sum property of a triangle states that the sum of the angles of a triangle is equal to 180º. A triangle has three sides and three angles, one at each vertex. Whether a triangle is an acute, obtuse, or a right triangle, the sum of its interior angles is always 180º.

Classifying triangles by their side lengths

Equilateral triangles

An$$\[\blueD{\text{equilateral}}\] equilateral triangle has three equal sides. Below are examples of equilateral triangles.

$\mathrm{}$\[10\]$\mathrm{}$\[10\]$\mathrm{}$\[10\]

$\mathrm{}$\[2\]$\mathrm{}$\[2\]$\mathrm{}$\[2\]

Isosceles triangles

An isosceles  triangle has at least two equal sides\[\purpleD{\text{two equal sides}}\]. Below are examples of isosceles triangles.

$\mathrm{}$\[5\]$\mathrm{}$\[4\]$\mathrm{}$\[5\]

$\mathrm{}$\[5\]$\mathrm{}$\[7\]$\mathrm{}$\[5\]

Scalene triangles

A scalene triangle has no equal sides. Below are examples of scalene triangles.

$\mathrm{}$\[9\]$\mathrm{}$\[7\]$\mathrm{}$\[6\]

$\mathrm{}$

Classifying triangles by their angles

Acute triangles

An acute triangle has 3 angles that each measure less than 90°
. Below are examples of acute triangles.

${\mathrm{}}^{}$\[\blueD{44^\circ}\]${\mathrm{}}^{}$\[\blueD{68^\circ}\]${\mathrm{}}^{}$\[\blueD{68^\circ}\]

${\mathrm{}}^{}$\[\blueD{60^\circ}\]${\mathrm{}}^{}$\[\blueD{60^\circ}\]${\mathrm{}}^{}$\[\blueD{60^\circ}\]

Right triangles

A right triangle has 1 angle that measures 90° and 2 acute angles. Below are examples of right triangles.

${\mathrm{}}^{}$\[\purpleD{90^{\circ}}\]${\mathrm{}}^{}$\[\gray{45^{\circ}}\]${\mathrm{}}^{}$\[\gray{45^{\circ}}\]

${\mathrm{}}^{}$\[\purpleD{90^\circ}\]${\mathrm{}}^{}$\[\gray{54^\circ}\]${\mathrm{}}^{}$\[\gray{36^\circ}\]

Obtuse triangles

An obtuse triangle has one angle that measures more than 90° and 2 acute angles. Below are examples of obtuse triangles.

$\mathrm{}$\[\gray{31°}\]$\mathrm{}$\[\gray{31°}\]$\mathrm{}$\[\greenD{118°}\]

${\mathrm{}}^{}$

III. Parallel and Perpendicular

Parallel lines are two or more lines that lie in the same plane and never intersect each other. They are equidistant from each other and have the same slope

Perpendicular lines are two distinct lines that intersect each other at 90°.

Classifying Geometric Shapes

https://www.splashlearn.com/math-vocabulary/geometry/quadrilateral

https://www.cuemath.com/geometry/quadrilaterals/

https://www.cuemath.com/geometry/properties-of-kite/

https://www.khanacademy.org/math/basic-geo/basic-geometry-shapes/x7fa91416:quadrilaterals-introduction/a/identify-quadrilaterals

https://www.cuemath.com/geometry/angle-sum-property/