Triangle And Circle Symmetry
Triangle And Circle Symmetry
Triangle:
A three sided figure is known as a triangle. There are different types of triangles based on the length of sides and angle, such as
Scalene Triangle:
It is a triangle in which all the three sides are of unequal length.
Symmetry of Scalene Triangle:
There is no line of symmetry in a scalene triangle as we can not draw any line which divides it into two equal parts.
Isosceles Triangle:
It is a triangle in which two sides are equal and angles opposite to equal sides are equal.
Symmetry of an Isosceles Triangle:
In an isosceles triangle, if we draw a perpendicular bisector to the side which is other than the equal sides. This line will pass through the vertex where the two equal sides are meeting as shown in the figure. This line divides the triangle into two equal parts. When we fold the isosceles triangle along this line the two parts will overlap each other. Hence this line will act as line of symmetry.
An isosceles triangle has one line of symmetry which is along the median through the vertex . In the figure below the equal sides are AB and AC. and the perpendicular bisector to the third side that is BC which passes through vertex A also known as Median AD is a line of symmetry of isosceles triangle ABC
Circle:
A geometrical figure whose each point is at the same distance from a fixed point is called a circle. The fixed point is called the center of the circle. and the distance is called radius of the circle. A straight line passing through the center and touching the circle at two points is called the diameter of the circle.
Symmetry of Circle:
In a circle the diameter divides the circle into two equal parts. and the two parts will overlap when we fold the circle along the diameter .This diameter acts as a line of symmetry for a circle. As there are infinite diameters to a circle.So we can say that a circle has infinite lines of symmetry.
Semi-Circle:
A geometrical figure which is made by cutting a circle along its diameter is called a semi-circle..
Symmetry of Semi-Circle:
A line which is perpendicular bisector of the base of the semi-circle divides the semi-circle into two equal parts. The two parts will overlap when we fold the semi-circle along this line .Thus this line acts as a line of symmetry for a semi-circle. As there is only one such line in a semi-circle.So we can say that a semi-circle has one line of symmetry.
Which of the following triangle has no line of symmetry . | |||
| Right Option : C | |||
| View Explanation | |||
In a triangle XYZ , XY = XZ and XM perpendicular YZ and ZP perpendicular XY. About which of the following is the triangle symmetrical? | |||
| Right Option : A | |||
| View Explanation | |||
How many lines of symmetry are there in an isosceles triangle? | |||
| Right Option : D | |||
| View Explanation | |||
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