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.

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

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