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By Giving a Counter Example, Show that the Following Statements Are Not True. P: If All the Angles of a Triangle Are Equal, Then the Triangle is an Obtuse Angled Triangle. - Mathematics

By giving a counter example, show that the following statements are not true.

p: If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.

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Solution

The given statement is of the form “if q then r”.

q: All the angles of a triangle are equal.

r: The triangle is an obtuse-angled triangle.

The given statement p has to be proved false. For this purpose, it has to be proved that if q, then ∼r.

To show this, angles of a triangle are required such that none of them is an obtuse angle.

It is known that the sum of all angles of a triangle is 180°. Therefore, if all the three angles are equal, then each of them is of measure 60°, which is not an obtuse angle.

In an equilateral triangle, the measure of all angles is equal. However, the triangle is not an obtuse-angled triangle.

Thus, it can be concluded that the given statement p is false.

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APPEARS IN

NCERT Class 11 Mathematics Textbook
Chapter 14 Mathematical Reasoning
Q 4.1 | Page 342
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