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:
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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 |
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