Question

In the given figure, PQR is an equilateral triangle, AB ║ PR and PR is produced to D such that RD = QA. Prove that BD bisects AR.​

Answer 1

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Answer 2

Given :

∆PQR is an equilateral triangle

AB ║ PR

RD = QA.

To Find :

BD bisects AR

Solution :

Since we are given that , ∆PQR is an equilateral triangle. Therefore all sides of ∆PQR will be equal to 60°. mathematically ;

→∠P + ∠Q + ∠R = 60°

Now, we are also provided that AB ║ PR Therefore :

→∠P = ∠R [Corresponding angles]

∴ ∠P = 60°

So, by observation we found that ∠P and ∠Q is equal to 69° therefore, the third side of the ∆ will also be 60°.

→∠Q + ∠A + ∠B = 60°

∴ ∆QAB is an equilateral traingle

→QB = AB

→QA = RD

→∠R = ∠M [Alternate angels]

∴ ∆ABM ≅ ∆RDM [AAS Property]

∴ AM = RM

∴BD bisects AR.

Hence Proved !