17. Find the valus of a and bi1. Two sides AB & BC and median AM of A

1.	17. Find the valus of a and bi1. Two sides AB & BC and median AM of A ABC are respectively equal to sides PO & QRand median PN of POR. Show that Î ABM,APONPage 2 of 4
Answer» Given: AM is the median of ∆ABC & PN is the median of ∆PQR. AB = PQ, BC = QR & AM = PN To Show: (i) ΔABM ≅ ΔPQN(ii) ΔABC ≅ ΔPQR Proof: Since AM & PN is the median of ∆ABC (i)1/2 BC = BM & 1/2QR = QN (AM and PN are median) Now, BC = QR. (given) ⇒ 1/2 BC = 1/2QR (Divide both sides by 2) ⇒ BM = QN In ΔABM and ΔPQN, AM = PN (Given) AB = PQ (Given) BM = QN (Proved above) Therefore, ΔABM ≅ ΔPQN (by SSS congruence rule) ∠B = ∠Q (CPCT) (ii)In ΔABC & ΔPQR, AB = PQ (Given) ∠B = ∠Q(proved above in part i)BC = QR (Given) Therefore, ΔABC ≅ ΔPQR ( by SAS congruence rule) hit like if you find it useful

17. Find the valus of a and bi1. Two sides AB & BC and median AM of A ABC are respectively equal to sides PO & QRand median PN of POR. Show that Î ABM,APONPage 2 of 4

Answer»

Given: AM is the median of ∆ABC & PN is the median of ∆PQR.

AB = PQ, BC = QR & AM = PN

To Show: (i) ΔABM ≅ ΔPQN(ii) ΔABC ≅ ΔPQR

Proof: Since AM & PN is the median of ∆ABC

(i)1/2 BC = BM & 1/2QR = QN (AM and PN are median) Now, BC = QR. (given)

⇒ 1/2 BC = 1/2QR (Divide both sides by 2) ⇒ BM = QN

In ΔABM and ΔPQN, AM = PN (Given) AB = PQ (Given) BM = QN (Proved above)

Therefore, ΔABM ≅ ΔPQN (by SSS congruence rule) ∠B = ∠Q (CPCT)

(ii)In ΔABC & ΔPQR,

AB = PQ (Given) ∠B = ∠Q(proved above in part i)BC = QR (Given) Therefore, ΔABC ≅ ΔPQR ( by SAS congruence rule)

hit like if you find it useful