CK-12 Geometry Concepts

5.5. Altitudes http://www.ck12.org

2. Draw the altitude for the triangle shown.


3. Draw the altitude for the triangle shown.

Answers:

1. Every triangle has three altitudes. For an obtuse triangle, at least one of the altitudes will be outside of the triangle,
   as shown in the picture at the beginning of this concept.


2. The triangle is an acute triangle, so the altitude is inside the triangle as shown below so that it is perpendicular to
   the base.


3. The triangle is a right triangle, so the altitude is already drawn. The altitude isX Z.

Practice

Write a two-column proof.

1.Given: Isosceles 4 ABCwith legsABandACBD⊥DCandCE⊥BEProve:BD∼=CE

For the following triangles, will the altitudes be inside the triangle, outside the triangle, or at the leg of the triangle?

2.

3.

4.

5.

6.

7. 4 JKLis an equiangular triangle.


8. 4 MNOis a triangle in which two the angles measure 30◦and 60◦.


9. 4 PQRis an isosceles triangle in which two of the angles measure 25◦.


10. 4 ST Uis an isosceles triangle in which two angles measures 45◦.

Given the following triangles, which line segment is the altitude?

11.

12.

13.

14.

15.

16.