Mathematics
In the following figures, the sides AB and BC and the median AD of the triangle ABC are respectively equal to the sides PQ and QR and median PS of the triangle PQR. Prove that △ ABC and △ PQR are congruent.
Related Questions
A triangle ABC has ∠B = ∠C. Prove that :
(i) the perpendiculars from the mid-point of BC to AB and AC are equal.
(ii) the perpendicular from B and C to the opposite sides are equal.
In the adjoining figure, QX and RX are the bisectors of the angles Q and R respectively of the triangle PQR. If XS ⊥ QR and XT ⊥ PQ; prove that :
(i) △ XTQ ≅ △ XSQ
(ii) PX bisects angle P.
In the following figure, OA = OC and AB = BC. Prove that :
(i) ∠AOB = 90°
(ii) △ AOD ≅ △ COD
(iii) AD = CD
The following figure shows a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN. Prove that :
(i) AM = AN
(ii) △ AMC ≅ △ ANB
(iii) BN = CM
(iv) △ BMC ≅ △ CNB
