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 |

**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.