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

1. Claim: "If all the angles of a triangle are equal, then the triangle is an obtuse angled triangle." Counter-example: An equilateral triangle has all three angles equal (each $60°$), satisfying the hypothesis. But each angle is $60° < 90°$, so it is an acute-angled triangle, not obtuse — the conclusion fails. Hence the claim is false.
2. Claim: "The equation $x^2 - 1 = 0$ does not have a root lying between 0 and 2." …

For each claim, find one specific instance satisfying the hypothesis (or, for a negative claim, directly satisfying …

• Assuming "all angles equal" must somehow force a large/obtuse angle — equal angles in a triangle in fact always sum to 60° each (since angles sum to 180°), giving an acute triangle. …