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In triangle ABC the right angle is at B. The altitude drawn from vertex A to side BC is:

Class 7The Triangle and its PropertiesTriangles
  • Athe side AB itself
  • Bthe side AC itself
  • Cthe segment from A to the midpoint of BC
  • Dthe side BC itself

Step-by-Step Solution

An altitude from A must be perpendicular to BC. Since angle B = 90°, AB is already perpendicular to BC, so AB IS the altitude from A — no extra segment needs to be drawn. Trap: choosing AC, the hypotenuse, which is not perpendicular to BC; or the segment to the midpoint of BC, which is the median, not the altitude.
Answer: A) the side AB itself

Key idea: Exterior angle property

Extend one side of a triangle past a vertex. The angle formed outside the triangle is the **exterior angle** at that vertex.

**Exterior angle = sum of the two opposite interior angles.**

So if the two non-adjacent interior angles are 50° and 60°, the exterior angle = 50° + 60° = 110°.

Why? The exterior angle and the adjacent interior angle form a linear pair (sum 180°), and the three interior angles also sum to 180°. Subtract: exterior = sum of the other two interior angles.

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