Kinds of polygons

Triangles. A triangle is a plane figure bounded by three straight lines and containing three angles. The sum of the angles of every triangle is 180°.

A triangle is identified by naming its vertices in any order. Thus, the triangle given in the figure 15 may be called ∆АВС, ∆BAC, ∆ВСA, ∆САВ, ∆CBA or ∆AСВ. The symbol ∆ means triangle.

Fig. 16 shows the various types of triangles. A scalene triangle (Fig. 15) is a triangle with no two sides equal. An isosceles triangle is a triangle which has two equal sides. The equal sides are called the legs; the third side is called the base. The angles at the base are called the base angles. The angle formed by the two equal sides, is called the vertex angle. An equilateral triangle is a triangle with all three sides equal.

Quadrilaterals. A quadrilateral is a plane figure bounded by four straight lines. There are several kinds of quadrilat­erals (Fig. 17).

A parallelogram is any quadrilateral in which two pairs of opposite sides are parallel.

A rectangle is a parallelogram whose angles are all right angles.

A square is a rectangle in which all the sides are equal in length.

A trapezoid is a quadrilateral in which only one pair of opposite sides are parallel.

The rectangle and the square both have four right angles. You have learned how to draw a 90º-angle with a protractor and construct the angle with" compasses. Using this knowl­edge, you can construct rectangles and squares.

Other Plane Figures (Fig. 18). A pentagon is a polygon which has five sides. A hexagon is a polygon which has six sides. An octagon is a polygon which has eight sides. A deca­gon is a polygon, which has six sides.

Since a regular polygon has equal sides and equal angles, all the vertices are equidistant from the centre.

A circle is a curved line a11 points of which are equidistant from the centre. Therefore, If we inscribe a regular polygon inside of a circle every vertex of the polygon will rest on the line of the circle.

Perimeter. The perimeter of a plane figure is the line around it. The perimeter of each the figures we have been studying would equal the sum of the lengths of its sides.

The perimeter of g rectangle equals two times the length plus two times the width

p = 2l + 2w or p = 2(l + w).

Since a square is a rectangle having four equal sides, we can represent each of the sides by the letter s. The perimeter of the square is expressed by the formula

p = s + s + s + s,

which is written as: p=4s.

The perimeter of a square equals the length of one side mul­tiplied by 4.