Mathematics
Statement 1: A polynomial whose one or more interior angle is less than two right angles is called a convex polygon.
Statement 2: The line joining any two consecutive vertex of a triangle of a polygon is called its diagonal.
Which of the following options is correct?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Geometrical Shapes
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Answer
A convex polygon is defined as a polygon in which all interior angles are less than 180°.
The statement suggests that if one or more interior angles are less than 180°, the polygon is convex. However, this is not sufficient. For a polygon to be convex, all interior angles must be less than 180°.
So, statement 1 is false.
A diagonal of a polygon is defined as a line segment connecting two non-consecutive vertices.
The line joining two consecutive vertices is simply a side of the polygon, not a diagonal.
So, statement 2 is false.
∴ Both the statements are false.
Hence, option 2 is the correct option.
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