Mathematics
Assertion (A): In a Δ ABC, if D is a point on the side BC such that AD divides BC in ratio AB : AC, then AD is the bisector of ∠A.
Reason (R): The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Similarity
1 Like
Answer
By angle bisector theorem,
The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
In a ΔABC, if AD is the internal angle bisector of ∠A, then it divides the opposite side BC in the ratio:
So, reason (R) is true.
In a ΔABC, if D is a point on the side BC such that AD divides BC in ratio AB : AC, then AD is the bisector of ∠A.
This is the converse of the Angle Bisector Theorem.
So, assertion (A) is true.
Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Hence, option 3 is the correct option.
Answered By
1 Like
Related Questions
In the given diagram, △ ABC ~ △ PQR and . The value of AB : PQ is :
8 : 3
3 : 5
3 : 8
5 : 8
In the given diagram, ∆ABC ∼ ∆PQR. If AD and PS are bisectors of ∠BAC and ∠QPR respectively then:
∆ABC ∼ ∆PQS
∆ABD ∼ ∆PQS
∆ABD ∼ ∆PSR
∆ABC ∼ ∆PSR
Given Δ ABC ∼ Δ PQR.
Assertion (A): If area of Δ ABC : area of Δ PQR = 16 : 25, then perimeter of Δ ABC : perimeter of Δ PQR = 4 : 5.
Reason (R): The ratio of perimeter of two similar triangle is equal to the ratio of their corresponding sides.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).
Given Δ PQR ∼ Δ DEF.
Assertion (A): If area of Δ PQR : area of Δ DEF = 9 : 49, then the ratio of their corresponding medians is also 4 : 9.
Reason (R): For the similar triangles, the ratio of their corresponding sides is equal to the ratio of their corresponding medians.
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.
Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).