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:**

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) |
1. (i) Given (ii) Common side. (iii) PS ⊥ QR. 2. By RHS criterion. 3. CPCTC. 4. PS bisects QR |

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