Ex 7.3, 3

Transcript

Ex 7.3,3 Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ∆ PQR (see figure ).Show that : ∆ ABM ≅ ∆ PQN Given: AB = PQ BC = QR & AM = PN Also, AM is the median of ∆ ABC So, BM = CM = 1/2 BC Also, PN is the median of ∆ PQR So, QN = RN = 1/2 QR To prove: ∆ ABM ≅ ∆ PQN Proof   Since BC = QR 1/2 BC = 1/2 QR BM = QN In ∆ ABM & ∆ PQN AB = PQ AM = PN BM = QN So, ∆ ABM ≅ ∆ PQN Ex 7.3,3 Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ∆ PQR (see figure ).Show that : (ii) ∆ ABC ≅ ∆ PQR From part (i), ∆ ABM ≅ ∆ PQN ∠B= ∠Q In ∆ ABC & ∆ PQR AB = PQ ∠B= ∠Q BC = QR So, ∆ ABC ≅ ∆ PQR