ALTITUDE OF A TRIANGLE
Definition Of Altitude Of A Triangle
Altitude of a Triangle is the perpendicular distance from any of its vertices to the opposite side. (This opposite side of the vertex is called the base of the altitude.)
More about Altitude of a Triangle
- As a triangle has 3 vertices, it has 3 altitudes.
- Altitudes can be used to find the area of the triangle.
Examples of Altitude of a Triangle
In the triangle ABC, AD is the perpendicular distance drawn from vertex A to the side BC. So, AD is the altitude of the triangle.
Video Examples: Altitude of a Triangle - MathHelp.com - Geometry Help
Solved Example on Altitude of a Triangle
Ques: Which of the figures shows an altitude of the triangle drawn?
Choices:
A. Figure 1
B. Figure 2
C. Figure 3
D. none of these
Correct Answer: C
Solution:
Step 1: Altitude of a triangle is the perpendicular distance from one of its vertices to its opposite side.
Step 2: The line drawn in Figure 3 from D to EF shows the perpendicular distance between D and EF.
Step 3: So, Figure 3 shows an altitude of the triangle drawn.
Quick Summary
- An altitude is a line segment from a vertex perpendicular to the opposite side.
- A triangle has three altitudes, one from each vertex.
- Altitudes can lie inside, outside, or on the triangle.
🍎 Teacher Insights
Use visual aids and hands-on activities to demonstrate altitudes. Emphasize the perpendicularity aspect using protractors and right angle tools. Relate it to area calculation to provide context.🎓 Prerequisites
- Basic understanding of triangles
- Knowledge of vertices and sides
- Concept of perpendicular lines
Check Your Knowledge
Q1: Which of the following is the altitude of triangle ABC, where AD is perpendicular to BC?
Q2: In a right triangle, which side can also be an altitude?
Frequently Asked Questions
Q: Can the altitude of a triangle be outside the triangle?
A: Yes, in obtuse triangles, the altitude from one of the acute angles falls outside the triangle.
Q: How do you find the altitude of a triangle?
A: The altitude can be found using trigonometric ratios, Pythagorean theorem, or by knowing the area and base length.