Hinglish

Altitudes of Triangles

Class 7 Maths · Chapter 7: A Tale of Three Intersecting Lines · NCERT Ganita Prakash section 7.4

Learn

The height of a tree or a person is measured straight up, at 90° to the ground. The height of vertex A above side BC is the length of the perpendicular AD from A to BC. The segment AD is an altitude of the triangle.

Every triangle has three altitudes, one from each vertex to the opposite side (AD, BE, CF). When we say "the height of the triangle", we mean the altitude to whichever side we choose as the base.

If the triangle leans over, the foot of the altitude may fall outside BC. Then extend BC and drop the perpendicular to the extended line. By paper folding, fold the triangle so the base folds onto itself through the top vertex: the crease is the altitude.

Accurately: use a ruler along the base and a set square sliding on it until its upright edge reaches the vertex; draw along that edge. In a right-angled triangle the two sides at the right angle are already perpendicular, so each is an altitude.

Explore: drawing an altitude.

  1. Put the steps for drawing the altitude from A in order.

Remember

  • An altitude is the perpendicular from a vertex to the opposite side (extended if needed).
  • A triangle has three altitudes; draw them with a ruler and set square.

Quick check

In which triangle can a side also be an altitude?

  1. right-angled
  2. equilateral
  3. every scalene triangle
  4. none
Answer

right-angled. The sides at the right angle are perpendicular to each other.

Think about it

Neel draws triangle TRY with ∠R = 140°. Where will the altitude from T to RY fall?

One answer

Outside RY: the triangle leans past R, so extend YR beyond R and drop the perpendicular from T onto it.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.