Which of these triangles is impossible to draw?

Class 7The Triangle and its PropertiesTriangles

AA scalene triangle containing an obtuse angle
BA triangle with two equal sides but all three angles different
CA right-angled triangle with two equal sides
DAn obtuse-angled triangle with two equal sides

Step-by-Step Solution

Angles opposite equal sides are equal, so two equal sides force two equal angles — "all three angles different" contradicts that. The others exist: 100°, 50°, 30° is obtuse scalene; 90°, 45°, 45° is right isosceles; 120°, 30°, 30° is obtuse isosceles. Trap: treating the side classification and the angle classification as unrelated, when equal sides carry an angle consequence.

Answer: B) A triangle with two equal sides but all three angles different

Key idea: Pythagoras theorem (right triangles only)

In a **right** triangle, the square of the hypotenuse equals the sum of the squares of the other two sides:

hypotenus

e^{2}

= side₁² + side₂²

Classic Pythagorean triple: 3, 4, 5 — because

3^{2} + 4^{2} = 9 + 16 = 25 = 5^{2}

.

Other triples to recognise: (5, 12, 13), (8, 15, 17), (7, 24, 25). The rule only applies when one of the angles is 90°. Never use Pythagoras for non-right triangles.

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