Question

Why are curved roads banked? Obtain an expression for an angle of banking for a curved road​

Answer 1

Given:

PQ=PR

QM and RN are the medians

To prove:

(i) ΔNQR = ΔMRQ

(ii) QM = RN

(iii) ΔPMQ = ΔPNR​

Solution:

We can prove these by following the given steps-

We know that PQR is an isosceles triangle.

PQ=PR

QM and RN divide PQ and PR into two equal parts

So, PN=NQ=PM=MR..(1)

i. In ∆NQR and ∆MRQ,

QR is the common side in both triangles.

Angle Q= Angle R (Angle corresponding to equal sides are equal)

NQ=MR (as per (1))

The triangles are congruent because of the SAS rule.

So, ΔNQR = ΔMRQ

ii. QM and RN are the sides of ∆NQR and ∆MRQ which are congruent.

So, QM=RN (corresponding sides of congruent triangles are equal)

iii. In ΔPMQ and ΔPNR​,

Angle P is common in both triangles.

PQ=PR (Isosceles triangle)

PN=PM (as per (1))

The triangles are congruent because of the SAS rule.

So, ΔPMQ = ΔPNR​

Therefore, ΔNQR = ΔMRQ, QM=RN, and ΔPMQ = ΔPNR​.

Answer 2

Answer:

hope it help you.

Thanks