Mathematics
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).
Related Questions
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).
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 ABC ∼ Δ DEF.
Assertion (A): If area of Δ ABC = 64 cm2, area of Δ DEF = 49 cm2 and BC = 4 cm, then EF is 7 cm.
Reason (R): The ratio of area of two similar triangle is equal to the ratio of square 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).
In the adjoining figure, ∠1 = ∠2 and ∠3 = ∠4. Show that PT × QR = PR × ST.
