Advertisements
Advertisements
प्रश्न
In the figure, ∠BCD = ∠ADC and ∠ACB =∠BDA. Prove that AD = BC and ∠A = ∠B.
उत्तर
∠BCD = ∠ADC
∠ACB = ∠BDA
∠BCD + ∠ACB = ∠ADC + ∠BDA
⇒ ∠ACD = ∠BDCACD = BDC
In ΔACD and ΔBCD
∠ACD =∠BDCACD = BDC
∠ADC = ∠BCD
ADC = BCD
CD = CD
Therefore, ΔACD ≅ ΔBCD ...(ASA criteria)
Hence, AD = BC and ∠A = ∠B.
APPEARS IN
संबंधित प्रश्न
In triangles ABC and PQR three equality relations between some parts are as follows:
AB = QP, ∠B = ∠P and BC = PR
State which of the congruence conditions applies:
In triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:
In the given figure, X is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then BY =
In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.
In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test?
If the following pair of the triangle is congruent? state the condition of congruency :
In ΔABC and ΔDEF, ∠B = ∠E = 90o; AC = DF and BC = EF.
In the following figure, OA = OC and AB = BC.
Prove that: AD = CD
The following figure 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: ΔAMC≅ ΔANB
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 triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side BC of ∆ABC so that the two triangles are congruent? Give reason for your answer.
