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In triangle DEF, DE = 8 cm, EF = 8 cm and DF = 5 cm. Which angle is the smallest?

Class 7The Triangle and its PropertiesTriangles
  • AAngle E
  • BAngle D
  • CAngle F
  • DAngle D and angle F are the smallest, and they are equal

Step-by-Step Solution

The smallest angle lies opposite the shortest side. The shortest side is DF = 5 cm, and the vertex opposite DF is E, so angle E is smallest. Angle D and angle F face the two equal 8 cm sides, so they are equal to each other and both larger. Trap: naming a vertex that lies ON the short side (D or F) instead of the vertex OPPOSITE it.
Answer: A) Angle E

Key idea: Side-angle relationship

**The longest side of a triangle is opposite the largest angle. The shortest side is opposite the smallest angle.**

In an isosceles triangle, the two equal sides face equal angles. In an equilateral triangle, all sides equal → all angles 60°.

This lets you order sides if you know the angles, or vice versa, even without computing exact values.

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