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) AM = AN (ii) ΔAMC ≅ ΔANB
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) In ΔAMC and ΔANB
AB = AC ...[ Given ] ...(1)
BM = CN ....[ Given ] ...(2)
Subtracting (2) from (1), we have
AB - BM = AC - CN
⇒ AM = AN ...(3)
(ii) Consider the triangles AMC and ANB
AC = AB ...[ given ]
∠AMC = ∠ANB ...[ common 90° ]
AM = AN ....[ from ( 3 ) ]
∴ By the Side-Angel-Side Criterion of congruence, we have ΔAMC ≅ ΔANB
APPEARS IN
RELATED QUESTIONS
In a ΔPQR, if PQ = QR and L, M and N are the mid-points of the sides PQ, QR and RP
respectively. Prove that: LN = MN.
In the given figure, if AE || DC and AB = AC, the value of ∠ABD is
In the given figure, if AC is bisector of ∠BAD such that AB = 3 cm and AC = 5 cm, then CD =
In ΔTPQ, ∠T = 65°, ∠P = 95° which of the following is a true statement?
In the following diagram, AP and BQ are equal and parallel to each other.
Prove that:
- ΔAOP ≅ ΔBOQ.
- AB and PQ bisect each other.
In ΔABC, AB = AC and the bisectors of angles B and C intersect at point O.Prove that BO = CO and the ray AO is the bisector of angle BAC.
In the figure, ∠BCD = ∠ADC and ∠ACB =∠BDA. Prove that AD = BC and ∠A = ∠B.
In ΔABC, AD is a median. The perpendiculars from B and C meet the line AD produced at X and Y. Prove that BX = CY.
If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles
Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.
∆ABC ≅ ∆LMN
