Advertisements
Advertisements
Question
The following figure has shown 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) BN = CM (ii) ΔBMC ≅ ΔCNB
Advertisements
Solution
In ΔABC, AB = AC. m and N are points on
AB and AC such that BM = CN
BN and CM are joined
(i) The corresponding parts of the congruent triangles are congruent.
∴ CM = BN ...[ c.p.c.t ] ...(1)
(ii) Consider the triangles ΔBMC and ΔCNB
BM = CN ...[Given]
BC = BC ...[Common]
CM = BN ...[From (1)]
∴ By Side-Side-Side criterion of congruence, we have ΔBMC ≅ ΔCNB
APPEARS IN
RELATED QUESTIONS
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
CDE is an equilateral triangle formed on a side CD of a square ABCD. Show that ΔADE ≅ΔBCE.
In the given figure, AB ⊥ BE and FE ⊥ BE. If BC = DE and AB = EF, then ΔABD is congruent to
State, whether the pairs of triangles given in the following figures are congruent or not:
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 8cm,BC = 6cm,∠B = 100°);
ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).
In ΔABC and ΔPQR and, AB = PQ, BC = QR and CB and RQ are extended to X and Y respectively and ∠ABX = ∠PQY. = Prove that ΔABC ≅ ΔPQR.
In the figure, BM and DN are both perpendiculars on AC and BM = DN. Prove that AC bisects BD.
In ΔABC, AB = AC. D is a point in the interior of the triangle such that ∠DBC = ∠DCB. Prove that AD bisects ∠BAC of ΔABC.
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side AB of ∆ABC so that the two triangles are congruent? Give reason for your answer.
Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.
∆YZX ≅ ∆PQR
