Altitude of an Equilateral Triangle is also a Median

Here we will prove that an altitude of an equilateral triangle is also a median.

In a ∆PQR, PQ = PR. Prove that the altitude PS is also a medina.

Solution:

Given in ∆PQR, PQ = PR and PS ⊥ QR.

Altitude of an Equilateral Triangle is also a Median

To prove PS is a median, i.e., QS = SR

Proof:

            Statement

1. In ∆PQS and ∆PRS,

(i) PQ = PR

(ii) PS = PS.

(iii) ∠PSQ = ∠PSR = 90°


2. ∆PQS ≅  ∆PRS

3. QS = SR

4. PS is a median. (Proved)

             Reasons

1.

(i) Given

(ii) Common side.

(iii) PS ⊥ QR.


2. By RHS criterion.

3. CPCTC.

4. PS bisects QR





9th Grade Math

From Prove that an Altitude of an Equilateral Triangle is also a Median to HOME PAGE




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.



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.




Share this page: What’s this?

Recent Articles

RSS

  1. Formation of Square and Rectangle | Construction of Square & Rectangle

    Jul 15, 25 02:46 AM

    Construction of a Square
    In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

    Read More

  2. 5th Grade Quadrilaterals | Square | Rectangle | Parallelogram |Rhombus

    Jul 15, 25 02:01 AM

    Square
    Quadrilaterals are known as four sided polygon.What is a quadrilateral? A closed figure made of our line segments is called a quadrilateral. For example:

    Read More

  3. Formation of Numbers | Smallest and Greatest Number| Number Formation

    Jul 14, 25 01:53 AM

    In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

    Read More

  4. 5th Grade Geometry Practice Test | Angle | Triangle | Circle |Free Ans

    Jul 14, 25 01:53 AM

    Name the Angles
    In 5th grade geometry practice test you will get different types of practice questions on lines, types of angle, triangles, properties of triangles, classification of triangles, construction of triang…

    Read More

  5. 5th Grade Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More