Properties of Shapes: Triangle, Quadrilateral, Pentagon, Hexagon

Triangle

A closed figure made by joining 3 non-collinear points bounded by three segments is called a triangle. Triangles are classified on the basis of their sides and angles.

On the basis of sides

1. Equilateral triangle: A triangle having all the sides of equal length.
2. Isosceles triangle: A triangle whose two sides are equal to each other and third is unequal.
3. Scalene triangle: A triangle whose all three sides are unequal to each other.

On the basis of Angles

1. Acute Angled Triangle: A triangle whose all 3 angles measure less than 90°.
2. Obtuse Angled Triangle: A triangle whose one angle measures greater than 90° but less than 180° . However, the other two angles measure less than 90°  .
3. Right Angled Triangle: A triangle whose one angle measures exactly 90° . However, the other two angles measure less than 90° .
4. Equiangular Triangle: A triangle whose all 3 angles are equal to each other i.e. they measure 60°

Quadrilateral

A closed figure bounded by 4 line segments is called a quadrilateral. It has 4 sides, 4 vertices, and 4 angles. The 2 sides meeting at a common vertex is called adjacent sides while the other 2 sides having uncommon vertices are called non-adjacent sides. The line segments joining any two non- adjacent vertices are called diagonals.

Types of Quadrilaterals

1. Rectangle: A quadrilateral whose opposite sides are equal and each angle is a right angle.
2. Square: A quadrilateral whose all sides are equal and each angle is a right angle.
3. Parallelogram: A quadrilateral whose opposite sides are equal and parallel.
4. Rhombus: A quadrilateral whose all sides are equal.
5. Trapezoid: A quadrilateral whose one pair of the opposite side is parallel.

Hexagon

A polygon made up of 6 line segments is called a hexagon. If all the sides and angles of the given hexagon are equal, then it is called a regular hexagon.

Example: State which of these figures are triangles and which are quadrilaterals:

Figure a,d represent triangles as they are made up of 3 line segments.

Figure b,c represent quadrilaterals as they are made up of 4 line segments.

Example: Classify the triangles on the basis of sides or angles:

Figure ‘a’ is a scalene triangle as all 3 sides are unequal.

Figure ‘b’ is an equilateral triangle as all 3 sides are equal to each other.

Figure ‘c’ is an obtuse-angled triangle as one angle measures greater than 90° .

Figure‘d’ is a right-angled triangle as one angle measures exactly 90° .

Example: Classify the polygons:

Figure ‘a’ is a parallelogram as its opposite sides are parallel.

Figure ‘b’ is a trapezoid as one pair of the opposite side is parallel.

Figure ‘c’ is a pentagon as it is made up of 5 line segments.

Figure ‘d’ is a quadrilateral as it is made up of 4 line segments.

Check Point

1. How many right angles can a triangle have?
2. Is it possible for a triangle to have 2 obtuse angles?
3. Identify the quadrilateral having only one pair of opposite sides parallel.
4. How many sides does a pentagon have?
5. Is the given figure a quadrilateral?

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