# 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.

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

Proof:

 Statement1. In ∆PQS and ∆PRS,(i) PQ = PR(ii) PS = PS.(iii) ∠PSQ = ∠PSR = 90°2. ∆PQS ≅  ∆PRS3. QS = SR4. PS is a median. (Proved) Reasons1.(i) Given(ii) Common side.(iii) PS ⊥ QR.2. By RHS criterion.3. CPCTC.4. PS bisects QR

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