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Which statement correctly distinguishes a median from an altitude of a triangle?

Class 7The Triangle and its PropertiesTriangles
  • AA median meets the opposite side at a right angle; an altitude ends at its midpoint.
  • BBoth always end at the midpoint of the opposite side.
  • CA median ends at the midpoint of the opposite side; an altitude meets that side, or its extension, at a right angle.
  • DBoth are always perpendicular to the opposite side.

Step-by-Step Solution

A median is defined by where it LANDS (the midpoint); an altitude is defined by the ANGLE it makes (90°). They coincide only in special cases, such as the median to the base of an isosceles triangle or any median of an equilateral triangle. Trap: swapping the two definitions, or assuming a median must also be perpendicular.
Answer: C) A median ends at the midpoint of the opposite side; an altitude meets that side, or its extension, at a right angle.

Key idea: Triangle inequality

**The sum of any two sides of a triangle is greater than the third side.**

So a triangle with sides 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3). But sides 1, 2, 5 do NOT form a triangle — 1 + 2 = 3 is less than 5, so the two short sides can't reach across.

Use this to test whether three given lengths can be a triangle, or to bound a missing side: if two sides are 5 and 8, the third must be greater than 8 − 5 = 3 AND less than 8 + 5 = 13.

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