Properties of Shapes (Triangle, Quadrilateral, Pentagon, Hexagon)

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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.
types of triangles based on sides

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°
triangles On the basis of Angles

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.
quadilaterals

Pentagon

A polygon made up of 5 line segments is called a pentagon. If all the sides and angles of the given pentagon are equal, then it is called a regular pentagon.

pentagon
hexagon

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.

facts on shapes

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

shapes

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:

shapes

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:

shapes

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?
shapes
Answer Key
  1. A right triangle can have only one right angle.
  2. No, an obtuse angle can have only one obtuse angle.
  3. Trapezoid
  4. 5
  5. No, the given figure is open.

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