Investigate the relationships between the altitude drawn from the right angle and perpendicular to the opposite side and other segments of the original right triangle.

The altitude of a triangle is a segment with one endpoint on a vertex of a triangle and perpendicular to the opposite side.

In the figure, BD is an altitude of ΔABC because one endpoint is at vertex B and it is perpendicular to AC, the side opposite B.

In a right triangle, when the altitude is drawn from the vertex of the right angle to the hypotenuse, the segment creates a right triangle with segments that have special relationships to one another.

The investigation begins...

This activity might not be viewable on your mobile device. Interactive exercise. Assistance may be required. Use this link to look more closely at the three triangles (count ‘em again!) in right triangle ABC.

Answer the following in your notes.

  1. How are the three triangles related?
  2. Use what you know about angle relationships to show that this is true for every right triangle with an altitude to the hypotenuse.
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Check Your Answer

When the altitude is has one endpoint at the vertex of the right angle and it is perpendicular to the hypotenuse the triangles created are similar to each other and to the original triangle. This is always true since the acute angles are complimentary and complements of congruent angles are congruent. The triangles are similar by AA. Close Pop Up