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
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to `bar(EF)`
BD and CE are bisectors of ∠B and ∠C of an isosceles ΔABC with AB = AC. Prove that BD = CE.
Mark the correct alternative in each of the following:
If ABC ≅ ΔLKM, then side of ΔLKM equal to side AC of ΔABC is
In the following figure, OA = OC and AB = BC.
Prove that: AD = CD
In the given figure, prove that:
(i) ∆ ACB ≅ ∆ ECD
(ii) AB = ED
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, AC = AE, AB = AD and ∠BAD = ∠EAC. Prove that BC = DE.
Prove that in an isosceles triangle the altitude from the vertex will bisect the base.
Given that ∆ABC ≅ ∆DEF List all the corresponding congruent sides
Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer.
