हिंदी में जवाब दो: Can a triangle have two right angles? Explain your reasoning.
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Step-by-Step Solution
Step 1: Sum of Angles in a Triangle
We know that the sum of the interior angles of any triangle is always equal to 180∘. This is a fundamental property of triangles.
Step 2: Assume Two Right Angles
Let's assume, for the sake of contradiction, that a triangle has two right angles. A right angle measures 90∘. So, let two angles of the triangle, say ∠A and ∠B, each be 90∘.
Step 3: Calculate Sum of Two Angles
If two angles are 90∘ each, their sum would be 90∘+90∘=180∘.
Step 4: Determine the Third Angle
According to the angle sum property, the third angle, ∠C, would be 180∘−(∠A+∠B). Substituting the sum of the two right angles, we get ∠C=180∘−180∘=0∘.
Step 5: Conclusion
A triangle must have three positive angles. An angle of 0∘ means that the two sides forming the angle would lie on top of each other, effectively collapsing the triangle into a line segment. Therefore, a triangle cannot have two right angles.