Prove that an Altitude of an Equilateral Triangle is also a Median

0
6


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.






Source link

LEAVE A REPLY

Please enter your comment!
Please enter your name here