Mathematics
Assertion (A): In the given figure, AB = BC and AD = CE, then BD = CE.
Reason (R): ΔBAD ≅ ΔBCE by SAS.
A is true, but R is false.
A is false, but R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.
Answer
It is given that AB = BC
⇒ ∠BAC = ∠BCA [Angles opposite to equal sides of the triangle are also equal]
⇒ ∠BAD = ∠BCE ………………(1)
In ΔBAD and ΔBCE,
⇒ AB = BC (Given)
⇒ AD = CE [Given]
⇒ ∠BAD = ∠BCE
∴ ΔBAD ≅ ΔBCE (By SAS congruency criterion)
By C.P.C.T.,
BE = BD
So, assertion (A) is false.
In ΔBAD and ΔBCE,
⇒ BD = BE (Proved above)
⇒ AB = BC (Given)
⇒ AD = EC (Given)
∴ ΔBAD ≅ ΔBCE (By SAS congruency criterion)
So, reason (R) is true.
Hence, option 2 is the correct option.
Related Questions
Statement (1): In the given figure, AC = DC = BD and ∠B = 30°.
Statement (2): ΔCAD is equilateral.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Statement (1): AB = AC and D is any point on side BC of triangle ABC.
Statement (2): AB > AD.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Assertion (A): In the given figure, S is any point on side QR.
∴ PQ + QR + RP > 2PS
Reason (R): In ΔPQS, PQ + QS > PS and in ΔPRS, PR + SR > PS
A is true, but R is false.
A is false, but R is true.
Both A and R are true and R is the correct reason for A.
Both A and R are true and R is the incorrect reason for A.
In the figure given alongside, AD = AB = AC, BD is parallel to CA and angle ACB = 65°. Find angle DAC.
