A polygon is a closed shape with three or more straight sides that connect at endpoints. Common polygons include triangles, which have three sides and interior angles, and quadrilaterals, which have four sides and interior angles. Triangles can be described based on their angles as acute, obtuse, or right triangles, or based on their sides as isosceles, equilateral, or scalene triangles. Quadrilaterals include rectangles, squares, parallelograms, and trapezoids, which differ based on properties of their sides and angles.

1. A polygon is a closed figure composed of three, four or more line segments
that connect at their end points; there is no limit to the number of sides it can
have.
• Each line segment is called the side
• The intersection at the endpoints is called the vertex
• The number of sides = the number of interior angles
• Polygons are named by the number of sides they have.
Two common polygons are the triangle and quadrilateral.
A triangle is a polygon having three sides and interior angles.
A quadrilateral is a polygon having four sides and interior angles.

2. We can describe triangles two ways: by the nature of their sides and by the
nature of their angles.
Let’s first look at describing triangles by their angles.
A triangle with three acute
angles is called an acute triangle.
0° < Angle < 90°
0° < Angle < 90°
A triangle with one obtuse angle
and two acute angles is called an
obtuse triangle.
90° < Angle < 180°
0° < Angle < 90°
A triangle with one right angle and two
acute angles is called a right triangle.
The side opposite the right angle is called 90°
the hypotenuse.

3. Next we will describe triangles by their sides.
An isosceles triangle has sides
with two equal lengths. 2” 2”
2.82”
3” 3” An equilateral triangle has
sides with three equal lengths.
3”
A scalene triangle has sides 1.5” 2.5”
with three different lengths.
2”

4. A quadrilateral is a four sided polygon. Here are some common quadrilaterals.
4”
A rectangle is a quadrilateral 90° 90°
where each set of opposite
sides are equal in length and
2” 2”
parallel to each other. All
four interior angles are 90°.
A square is just a special 90° 90°
rectangle of four equal sides.
4”
A parallelogram is a quadrilateral where
3” each set of opposite sides are equal in length
135° 45° and parallel (just like a rectangle). The
1.4”
1.4” opposite interior angles are the same
45° 135° measure.
3” Both rectangles and squares are special
types of parallelograms.
A trapezoid is a quadrilateral where only Top & bottom
one pair of opposite sides are parallel. parallel, sides are not