Geometrical Property of Altitudes

Here we will discuss about a geometrical property of altitudes.

The three altitudes of triangle are concurrent. The point at which they intersect is known as the orthocentre of the triangle.

In the adjoining figure, the three altitudes XP, YQ and ZR intersect at the orthocentre O.

In the adjoining figure ∆XYZ is a right-angled triangle. Here we see that XY ⊥ YZ, YZ ⊥ XY and YM ⊥ XZ.

Thus, the three altitudes XY, YZ and YM intersect at Y. So, Y is the orthocentre of ∆XYZ.

In an obtuse-angled ∆XYZ, the altitudes with respect to XY, YZ and ZX are ZR, XP and YQ respectively.

The altitudes when produced, meet at O. The O is the orthocentre of ∆XYZ.

We see that the orthocentre may lie within, on or outside the triangle.

9th Grade Math

From Geometrical Property of Altitudes to HOME PAGE

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. Method of H.C.F. |Highest Common Factor|Factorization &Division Method

    Apr 13, 24 05:12 PM

    HCF by Short Division Method
    We will discuss here about the method of h.c.f. (highest common factor). The highest common factor or HCF of two or more numbers is the greatest number which divides exactly the given numbers. Let us…

    Read More

  2. Factors | Understand the Factors of the Product | Concept of Factors

    Apr 13, 24 03:29 PM

    Factors of a number are discussed here so that students can understand the factors of the product. What are factors? (i) If a dividend, when divided by a divisor, is divided completely

    Read More

  3. Methods of Prime Factorization | Division Method | Factor Tree Method

    Apr 13, 24 01:27 PM

    Factor Tree Method
    In prime factorization, we factorise the numbers into prime numbers, called prime factors. There are two methods of prime factorization: 1. Division Method 2. Factor Tree Method

    Read More

  4. Divisibility Rules | Divisibility Test|Divisibility Rules From 2 to 18

    Apr 13, 24 12:41 PM

    Divisibility Rules
    To find out factors of larger numbers quickly, we perform divisibility test. There are certain rules to check divisibility of numbers. Divisibility tests of a given number by any of the number 2, 3, 4…

    Read More

  5. Even and Odd Numbers Between 1 and 100 | Even and Odd Numbers|Examples

    Apr 12, 24 04:22 PM

    even and odd numbers
    All the even and odd numbers between 1 and 100 are discussed here. What are the even numbers from 1 to 100? The even numbers from 1 to 100 are:

    Read More